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cleartomark
%%EndFont 
%%BeginFont: CMBX7
%!PS-AdobeFont-1.1: CMBX7 1.0
%%CreationDate: 1991 Aug 20 16:35:49
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 53 /five put
readonly def
/FontBBox{-55 -250 1289 751}readonly def
/UniqueID 5000765 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 175 /fi put
dup 183 /caron put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 89 /Y put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 122 /z put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX6
%!PS-AdobeFont-1.1: CMBX6 1.0
%%CreationDate: 1991 Aug 20 16:35:30
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
readonly def
/FontBBox{-49 -250 1367 753}readonly def
/UniqueID 5000764 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX9
%!PS-AdobeFont-1.1: CMBX9 1.0
%%CreationDate: 1991 Aug 20 16:36:25
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 71 /G put
dup 72 /H put
dup 78 /N put
dup 79 /O put
dup 80 /P put
readonly def
/FontBBox{-58 -250 1195 750}readonly def
/UniqueID 5000767 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: MSAM10
%!PS-AdobeFont-1.1: MSAM10 2.1
%%CreationDate: 1993 Sep 17 09:05:00
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSAM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 164 /square put
dup 178 /satisfies put
dup 40 /multimap put
dup 66 /triangleright put
dup 70 /star put
dup 112 /rightanglenw put
dup 113 /rightanglene put
readonly def
/FontBBox{8 -463 1331 1003}readonly def
/UniqueID 5031981 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: MSAM7
%!PS-AdobeFont-1.1: MSAM7 2.1
%%CreationDate: 1992 Oct 17 08:30:29
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSAM7) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSAM7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 112 /rightanglenw put
dup 113 /rightanglene put
readonly def
/FontBBox{0 -576 1569 1076}readonly def
/UniqueID 5032012 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /prime put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 189 /braceleftbigg put
dup 83 /uniontext put
dup 119 /arrowvertexdbl put
dup 196 /arrowdblbt put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX8
%!PS-AdobeFont-1.1: CMBX8 1.0
%%CreationDate: 1991 Aug 20 16:36:07
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX8 def
/PaintType 0 def
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
dup 50 /two put
dup 51 /three put
readonly def
/FontBBox{-59 -250 1235 750}readonly def
/UniqueID 5000766 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
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cleartomark
%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
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2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C
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cleartomark
%%EndFont 
%%BeginFont: CMSY9
%!PS-AdobeFont-1.1: CMSY9 1.0
%%CreationDate: 1991 Aug 15 07:22:27
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 56 /universal put
dup 57 /existential put
dup 94 /logicaland put
readonly def
/FontBBox{-30 -958 1146 777}readonly def
/UniqueID 5000819 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
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cleartomark
%%EndFont 
%%BeginFont: CMSS9
%!PS-AdobeFont-1.1: CMSS9 1.0
%%CreationDate: 1991 Aug 20 17:34:24
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSS9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMSS9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 69 /E put
dup 73 /I put
dup 76 /L put
dup 82 /R put
dup 97 /a put
dup 120 /x put
readonly def
/FontBBox{-63 -250 1027 760}readonly def
/UniqueID 5000802 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
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1921070EA097CAAAE9E4E9D5D21DB9363555AD932858E23A534F7DA9F2F0E79E
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87C58CC2A2332C96EA8E05E67723F2D28FCE8B6D8C295985FE8359B52A645D56
C7F2DD022508C8DFA5053F401CA7F14DFCEACCC8F15A8CF1880AB0F4917A45A6
EFE44B768A10B0E28325218B7A799275C34AD0976DB70A262FCE86FF006F3FA6
221F0E4DB5D7A5F409059024875248ADBA784B11E7FAFD6E07307E07AA08A563
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333C17048CDE1B90D97737519C92E72E194178AB092BA65F48DF95B63C4FCCA1
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cleartomark
%%EndFont 
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMCSC10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 183 /caron put
dup 45 /hyphen put
dup 68 /D put
dup 69 /E put
dup 73 /I put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 83 /S put
dup 84 /T put
dup 88 /X put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
readonly def
/FontBBox{14 -250 1077 750}readonly def
/UniqueID 5000772 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBXTI10
%!PS-AdobeFont-1.1: CMBXTI10 1.0
%%CreationDate: 1991 Aug 18 17:46:30
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBXTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMBXTI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 77 /M put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 97 /a put
dup 98 /b put
dup 100 /d put
dup 101 /e put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
readonly def
/FontBBox{-29 -250 1274 754}readonly def
/UniqueID 5000771 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 42 /notsubseteql put
dup 50 /notsatisfies put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSSI10
%!PS-AdobeFont-1.1: CMSSI10 1.0
%%CreationDate: 1991 Aug 20 17:34:37
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSSI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -12 def
/isFixedPitch false def
end readonly def
/FontName /CMSSI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 99 /c put
dup 101 /e put
dup 110 /n put
dup 111 /o put
readonly def
/FontBBox{-97 -250 1077 759}readonly def
/UniqueID 5000810 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
dup 50 /two put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /minus put
dup 162 /periodcentered put
dup 163 /multiply put
dup 167 /plusminus put
dup 173 /circlemultiply put
dup 178 /bullet put
dup 180 /equivalence put
dup 181 /reflexsubset put
dup 183 /lessequal put
dup 184 /greaterequal put
dup 185 /precedesequal put
dup 187 /similar put
dup 188 /approxequal put
dup 189 /propersubset put
dup 195 /arrowleft put
dup 33 /arrowright put
dup 41 /arrowdblright put
dup 44 /arrowdblboth put
dup 50 /element put
dup 54 /negationslash put
dup 55 /mapsto put
dup 56 /universal put
dup 57 /existential put
dup 58 /logicalnot put
dup 59 /emptyset put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 73 /I put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 91 /union put
dup 92 /intersection put
dup 93 /unionmulti put
dup 94 /logicaland put
dup 95 /logicalor put
dup 96 /turnstileleft put
dup 100 /ceilingleft put
dup 101 /ceilingright put
dup 102 /braceleft put
dup 103 /braceright put
dup 104 /angbracketleft put
dup 105 /angbracketright put
dup 106 /bar put
dup 110 /backslash put
dup 118 /subsetsqequal put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSS8
%!PS-AdobeFont-1.1: CMSS8 1.0
%%CreationDate: 1991 Aug 20 17:34:12
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSS8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMSS8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 53 /five put
dup 105 /i put
dup 110 /n put
readonly def
/FontBBox{-65 -250 1062 761}readonly def
/UniqueID 5000801 def
currentdict end
currentfile eexec
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%%EndFont 
%%BeginFont: CMMI7
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%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
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readonly def
/FontBBox{0 -250 1171 750}readonly def
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currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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0 1 255 {1 index exch /.notdef put} for
dup 174 /alpha put
dup 175 /beta put
dup 177 /delta put
dup 178 /epsilon1 put
dup 181 /theta put
dup 186 /nu put
dup 187 /xi put
dup 188 /pi put
dup 189 /rho put
dup 190 /sigma put
dup 193 /phi put
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dup 59 /comma put
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dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
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readonly def
/FontBBox{-32 -250 1048 750}readonly def
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currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSS10
%!PS-AdobeFont-1.1: CMSS10 1.0
%%CreationDate: 1991 Aug 20 17:33:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSS10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMSS10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 44 /comma put
dup 45 /hyphen put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 78 /N put
dup 80 /P put
dup 83 /S put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
readonly def
/FontBBox{-61 -250 999 759}readonly def
/UniqueID 5000803 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 162 /Delta put
dup 166 /Pi put
dup 167 /Sigma put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 185 /macron put
dup 34 /quotedblright put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 63 /question put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 94 /circumflex put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 196 /dieresis put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 185 /macron put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 61 /equal put
dup 196 /dieresis put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI6
%!PS-AdobeFont-1.1: CMMI6 1.100
%%CreationDate: 1996 Jul 23 07:53:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 65 /A put
dup 66 /B put
dup 69 /E put
dup 97 /a put
dup 98 /b put
dup 101 /e put
dup 107 /k put
dup 108 /l put
dup 120 /x put
dup 121 /y put
readonly def
/FontBBox{11 -250 1241 750}readonly def
/UniqueID 5087381 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY6
%!PS-AdobeFont-1.1: CMSY6 1.0
%%CreationDate: 1991 Aug 15 07:21:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /prime put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
/UniqueID 5000816 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /minus put
dup 164 /asteriskmath put
dup 48 /prime put
dup 73 /I put
dup 82 /R put
dup 83 /S put
dup 106 /bar put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 189 /rho put
dup 58 /period put
dup 59 /comma put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 69 /E put
dup 70 /F put
dup 73 /I put
dup 75 /K put
dup 80 /P put
dup 93 /sharp put
dup 97 /a put
dup 98 /b put
dup 101 /e put
dup 102 /f put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 122 /z put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX12
%!PS-AdobeFont-1.1: CMBX12 1.0
%%CreationDate: 1991 Aug 20 16:34:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 175 /fi put
dup 183 /caron put
dup 45 /hyphen put
dup 46 /period put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 65 /A put
dup 66 /B put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 89 /Y put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueID 5000769 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMTI10
%!PS-AdobeFont-1.1: CMTI10 1.00B
%%CreationDate: 1992 Feb 19 19:56:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 175 /fi put
dup 176 /fl put
dup 182 /acute put
dup 183 /caron put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 58 /colon put
dup 59 /semicolon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 87 /W put
dup 89 /Y put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueID 5000828 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 44 /comma put
dup 46 /period put
dup 48 /zero put
dup 50 /two put
dup 52 /four put
dup 58 /colon put
dup 68 /D put
dup 77 /M put
dup 78 /N put
dup 82 /R put
dup 83 /S put
dup 86 /V put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 118 /v put
dup 119 /w put
dup 122 /z put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec
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@start /Fa 129[636 6[636 1[636 636 636 636 1[636 636
636 636 2[636 1[636 1[636 636 636 636 1[636 38[636 10[636
636 46[{}20 1212.12 /CMTT10 rf /Fb 202[502 53[{}1 774.872
/CMBX7 rf /Fc 175[870 80[{}1 1106.96 /CMBX10 rf /Fd 199[461
461 461 461 461 461 461 461 49[{}8 664.176 /CMBX6 rf
/Fe 175[805 886 921 5[921 926 71[{}5 996.264 /CMBX9 rf
/Ff 189[861 66[{}1 1106.96 /MSAM10 rf /Fg 142[470 470
112[{}2 885.568 /MSAM7 rf /Fh 207[255 48[{}1 774.872
/CMSY7 rf /Fi 128[943 7[943 35[1010 56[909 26[{}4 1212.12
/CMEX10 rf /Fj 204[542 542 542 49[{}3 885.568 /CMBX8
rf /Fk 205[406 406 406 4[621 43[{}4 664.176 /CMR6 rf
/Fl 161[683 36[569 569 56[{}3 996.264 /CMSY9 rf /Fm 135[472
22[492 14[663 5[558 2[286 3[615 69[{}6 996.264 /CMSS9
rf /Fn 167[987 3[953 3[899 1[987 1199 3[492 3[899 1005
22[458 45[{}9 1212.12 /CMCSC10 rf /Fo 138[752 467 590
608 2[716 788 1145 360 645 431 431 3[645 716 1[645 716
16[954 80[{}16 1212.12 /CMBXTI10 rf /Fp 205[741 7[943
42[{}2 1212.12 /MSBM10 rf /Fq 144[606 626 8[539 1[539
99[{}4 1212.12 /CMSSI10 rf /Fr 205[441 441 49[{}2 774.872
/CMR7 rf /Fs 172[1036 1370 4[1710 77[{}3 1594.02 /CMBXTI10
rf /Ft 137[861 12[430 430 553 553 7[738 34[553 1[615
6[738 16[1107 22[861 8[307 861{}13 1106.96 /CMSY10 rf
/Fu 205[412 412 412 48[{}3 774.872 /CMSS8 rf /Fv 154[420
461 1[389 480 27[650 1[635 669 666 65[{}8 774.872 /CMMI7
rf /Fw 133[515 543 633 792 537 634 400 519 2[557 1[664
972 1[576 1[381 2[542 515 2[475 585 12[647 679 841 875
711 844 889 4[487 920 2[817 1[791 840 830 3[553 1[307
307 25[721 1[660 4[631 1[547 23[{}37 1106.96 /CMMI10
rf /Fx 134[510 1[756 1[572 400 424 378 1[572 553 572
4[264 3[492 572 492 1[532 13[615 2[707 1[784 2[769 1[307
1[738 2[799 1[738 738 65[{}23 1106.96 /CMSS10 rf /Fy
134[584 2[584 615 1[437 434 1[615 553 615 922 307 584
338 307 1[553 1[492 615 492 615 553 3[307 1[307 10[753
8[869 4[784 830 3[861 2[307 3[553 1[553 553 553 553 2[307
4[430 430 19[553 20[{}36 1106.96 /CMR10 rf /Fz 145[486
4[224 51[470 1[470 470 470 470 48[{}7 885.568 /CMSS8
rf /FA 142[606 606 41[1145 3[943 25[1347 24[741 11[943
3[{}7 1212.12 /MSAM10 rf /FB 128[470 65[732 9[470 470
470 470 4[732 1[366 366 17[470 22[{}10 885.568 /CMR8
rf /FC 134[420 464 11[267 439 5[391 2[364 448 27[598
2[615 614 65[{}10 664.176 /CMMI6 rf /FD 207[243 48[{}1
664.176 /CMSY6 rf /FE 149[261 22[570 803 8[518 24[255
44[470 2[732{}7 885.568 /CMSY8 rf /FF 133[438 6[435 425
2[455 571 832 281 490 381 320 2[452 436 2[403 500 3[366
12[597 4[793 1[408 2[595 690 1[671 710 705 5[261 261
31[482 26[{}26 885.568 /CMMI8 rf /FG 129[606 3[564 594
693 868 588 694 438 568 547 541 610 588 728 1064 362
631 499 418 698 578 593 564 631 525 520 641 3[471 2[827
704 1004 1[707 1[708 743 920 958 778 925 974 1176 825
1029 1[533 1008 953 779 895 1004 866 919 909 3[606 1[337
337 27[722 2[693 627 691 530 599 4[569 2[492 539 1[686
775 11[{}65 1212.12 /CMMI10 rf /FH 132[897 797 3[946
996 697 707 732 1[996 897 996 1494 498 946 548 498 996
897 548 818 996 797 1[872 7[1354 3[1378 1247 996 1338
1[1225 1347 1402 1701 1077 1[926 1[1402 1[1127 1177 1374
2[1354 9[897 897 897 897 897 897 897 2[498 598 24[897
7[996 12[{}49 1594.02 /CMBX12 rf /FI 137[943 7[606 3[337
471 471 606 606 539 539 3[741 808 808 808 808 808 6[660
734 1027 1[843 965 5[660 4[935 638 796 968 5[606 808
673 673 0 0 3[808 5[1212 2[1212 7[1212 1212 5[943 943
943 1[943 943 943 1[943 943 1[606 4[943 3[943 3[943 337
943{}50 1212.12 /CMSY10 rf /FJ 137[1363 6[1291 2[717
1[789 2[1291 1[1178 3[1256 16[1764 25[1291 1291 1291
1291 1291 1291 49[{}14 2295.84 /CMBX12 rf /FK 132[620
496 589 562 805 558 651 403 496 511 1[620 620 681 991
310 558 372 372 620 558 372 558 620 558 558 620 6[743
901 1[1211 1[901 867 681 884 1[822 929 901 1087 760 932
636 467 901 1[791 822 915 867 853 901 5[372 372 5[620
620 620 620 620 620 372 434 372 2[496 496 19[620 620
5[712 681 12[{}65 1212.12 /CMTI10 rf /FL 133[620 2[1007
736 774 542 550 574 1[774 697 774 1162 387 736 426 387
774 697 426 639 774 620 774 678 7[1054 3[1072 970 774
1045 1[953 1[1091 1323 838 1093 1[529 1091 2[916 1069
1007 1[1054 6[387 697 697 697 697 697 697 697 697 697
697 2[465 387 2[542 542 19[697 7[774 12[{}56 1212.12
/CMBX10 rf /FM 133[1377 1635 2[1635 1721 1205 1222 1265
1[1721 1549 1721 2582 861 1635 947 861 1721 1549 947
1414 1721 1377 1721 1506 6[1893 4[2381 2155 1721 5[2939
1[2426 8[2203 45[1549 7[1721 12[{}32 2754.12 /CMBX12
rf /FN 134[559 559 828 559 626 438 465 414 1[626 606
626 963 290 593 323 290 626 606 1[539 626 539 1[582 13[673
2[774 1[859 2[842 1[337 859 808 2[875 774 808 808 19[404
337 44[{}35 1212.12 /CMSS10 rf /FO 128[606 3[606 539
640 640 875 640 673 471 478 475 640 673 606 673 1010
337 640 370 337 673 606 370 539 673 539 673 606 2[606
337 1[337 741 909 909 1246 909 909 875 673 892 943 825
943 909 1111 758 943 623 438 909 951 791 825 926 875
859 909 1[572 1[943 1[337 337 606 606 606 606 606 606
606 606 606 606 606 337 404 337 943 1[471 471 337 4[606
11[606 1[606 606 606 4[673 673 707 4[875 909 3[1010 1[{}90
1212.12 /CMR10 rf /FP 141[506 10[650 1[578 2[723 650
6[795 37[650 1[650 1[650 1[361 1[361 44[{}11 1328.35
/CMR12 rf /FQ 139[837 849 879 1[1196 1076 1196 1[598
1136 658 598 1[1076 1[982 1196 2[1046 19[2041 64[1196
12[{}16 1912.83 /CMBX12 rf /FR 133[694 2[1127 824 1[607
616 607 1[867 780 867 1[434 824 477 434 1[780 477 694
867 694 1[780 10[1170 2[867 1149 3[1170 1430 8[1192 9[434
11[434 46[{}27 1594.02 /CMR12 rf /FS 137[815 815 785
608 800 2[844 815 992 682 844 564 401 1[852 711 741 829
785 770 815 6[889 6[812 2[985 2[1314 31[502 24[734 20[{}25
1328.35 /CMCSC10 rf end
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TeXDict begin HPSdict begin 1 0 bop 14832 7181 a FS(Sveu)18040
7070 y(\267)18015 7181 y(cili)20221 7070 y(\267)20284
7181 y(ste)502 b(u)g(Za)-30 b(grebu)9985 9317 y(Prir)g(odoslo)g(vno-ma)
-89 b(tema)g(ti)26711 9206 y(\267)26686 9317 y(cki)506
b(f)-118 b(akul)-89 b(tet)16258 11452 y(Ma)g(tema)g(ti)22753
11341 y(\267)22728 11452 y(cki)503 b(odjel)18719 28706
y FR(Nev)-87 b(a)520 b(Slani)2435 34935 y FQ(Mo)60 b(deli)683
b(apstraktne)e(kriptogra\257je)g(i)i(protok)-60 b(oli)17019
39590 y FR(Magistarski)520 b(rad)17409 56844 y(V)-130
b(o)43 b(ditelj)520 b(rada:)12886 58682 y(prof.dr.sc.)692
b(Dean)521 b(Rosenzw)-43 b(eig)18531 70330 y FP(Zagreb,)434
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%%Page: 3 3
TeXDict begin HPSdict begin 3 2 bop 13939 55892 a FO(Ne)-64
b(\267)-542 b(sto)330 b(sasvim)f(malo,)344 b(toplo)329
b(i)g(nje)-34 b(\267)-572 b(zno,)345 b(na)329 b(primjer)g("h)-34
b(v)-67 b(ala",)13939 57397 y(onima)990 b(iz)f(mo)67
b(je)990 b FN(K)p FO(-ljusk)-34 b(e:)1710 b(obitelji,)1136
b(matemati)-34 b(\267)-572 b(ck)-34 b(o)67 b(j)13939
58903 y(obitelji,)404 b(prijateljima.)13939 60408 y(P)-34
b(osebno,)505 b(vjernim)451 b(\267)-572 b(cita)-34 b(\267)-572
b(cima,)469 b(\267)-572 b(ciji)484 b(se)g(stru)-34 b(\267)-572
b(cni)485 b(k)-34 b(omen)g(tari,)13939 61913 y(kritik)g(e)515
b(i)g(p)34 b(o)g(dr)-64 b(\267)-542 b(sk)-67 b(a)515
b(nalaze)g(na)h(sv)-67 b(ak)-34 b(o)67 b(j)516 b(stranici)f(i)482
b(\267)-572 b(ciji)515 b(sam)13939 63419 y(v)-34 b(eseli)305
b(du)-34 b(\267)-572 b(znik,)325 b(a)305 b(to)h(su:)490
b(Dean)305 b(Rosenzw)-34 b(eig,)325 b(v)-34 b(o)34 b(ditelj)306
b(rada,)13939 64924 y(P)-34 b(aola)405 b(Gla)-34 b(v)-67
b(an,)403 b(F)-101 b(rancisco)404 b(Martins.)13939 66430
y(Desculpa)439 b(aos)g(to)34 b(dos)439 b(que)f(p)34 b(edi)438
b(de)h(esp)34 b(erar)437 b(p)34 b(or)439 b(mim)f(p)34
b(or)13939 67935 y(causa)405 b(da)f(maldita)h(coisa)e(que)h(n)-34
b(unca)406 b(acaba)-34 b(v)-67 b(a.)13939 69441 y(Querido)586
b(F)-101 b(ranci,)630 b(obrigada)586 b(p)34 b(or)586
b(tudo,)632 b(que)585 b(deste,)631 b(p)34 b(ela)13939
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%%Page: 5 5
TeXDict begin HPSdict begin 5 4 bop 2435 16050 a FM(Sadr)-86
b(\267)-1463 b(za)172 b(j)2435 23221 y FL(1)1121 b(Uv)-39
b(o)39 b(d)34057 b(7)2435 25964 y(2)1121 b(Kriptografski)465
b(protok)-39 b(oli)465 b(i)g(njiho)-39 b(vi)466 b(apstraktni)e(mo)39
b(deli)6595 b(9)4253 27485 y FO(2.1)1239 b(Enkrip)34
b(cijsk)-34 b(e)404 b(sheme)612 b(.)606 b(.)g(.)g(.)f(.)h(.)g(.)g(.)f
(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)1837
b(9)4253 29006 y(2.2)1239 b(F)-101 b(ormalni)404 b(mo)34
b(deli)1165 b(.)605 b(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f
(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)1231 b(11)4253
30527 y(2.3)1239 b(F)-101 b(amozni)405 b(Needham-Sc)-34
b(hro)34 b(eder)1027 b(.)606 b(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)g(.)f(.)h(.)g(.)g(.)1231 b(14)4253 32047 y(2.4)1239
b(Pretp)34 b(osta)-34 b(vk)g(e)405 b(i)e(zah)-34 b(tjevi)405
b(na)f(apstraktne)h(mo)34 b(dele)845 b(.)605 b(.)h(.)g(.)g(.)f(.)h(.)g
(.)g(.)1231 b(15)4253 33568 y(2.5)1239 b(Prezen)-34 b(tirani)404
b(apstraktni)h(mo)34 b(deli)1151 b(.)605 b(.)h(.)g(.)g(.)f(.)h(.)g(.)g
(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)1231 b(17)2435 36311
y FL(3)1121 b(T)-116 b(ransformacije)463 b(m)-39 b(ultiskup)39
b(o)-39 b(v)-77 b(a)19056 b(19)4253 37832 y FO(3.1)1239
b(Jezik)561 b(.)606 b(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)
g(.)1231 b(19)4253 39353 y(3.2)1239 b(Opis)404 b(protok)-34
b(ola)1075 b(.)606 b(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)
f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)1231
b(23)4253 40874 y(3.3)1239 b(Sp)34 b(eci\257k)-67 b(acija)404
b(Dolev{Y)-101 b(ao)403 b(protok)-34 b(ola)357 b(.)606
b(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)g(.)1231
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b(v)g(oljno)440 b FK(je)-62 b(dnostavna)462 b(za)i(izr)-62
b(a)-31 b(\267)-589 b(cunati)p FO(,)444 b(p)34 b(o)-64
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%%Page: 10 10
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b(i)i(eksp)34 b(onenciranje)404 b(u)h FG(p)p FO(-grupama.)7749
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b(cijskih)404 b(shema:)9567 38898 y FI(\262)606 b FK(asimetri)-31
b(\267)-589 b(cne)493 b FO(ili)403 b(enkrip)34 b(cijsk)-34
b(e)403 b(sheme)h FK(javno)-62 b(ga)432 b(klju)-31 b(\267)-589
b(ca)93 b FO(;)9567 41807 y FI(\262)606 b FK(simetri)-31
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b(klju)-34 b(\267)-572 b(c,)524 b FK(privatni)d(klju)-31
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b(v)g(om)502 b(vlas-)7749 49232 y(niku.)659 b(Tk)-34
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b(\267)-572 b(c,)637 b FK(zaje)-62 b(dni)-31 b(\267)-589
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y(10)p eop end end
%%Page: 11 11
TeXDict begin HPSdict begin 11 10 bop 4317 7181 a FO(Konkretni)549
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b(olima,)722 b(b)34 b(ez)658 b(obzira)f(na)2435 41177
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%%Page: 12 12
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b(arna)421 b(situacija.)592 b(T)-101 b(o)422 b(je)g(ono)358
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51785 y(tuitivnost)356 b(neformalnog)f(rasu)p 22611 51172
V(div)-67 b(anja,)365 b(a)355 b(snab)34 b(djev)-34 b(en)356
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b(cnim)7749 53291 y(deduktivnim)404 b(aparatom.)9631
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%%Page: 13 13
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b(diskutiramo)g(k)-67 b(asnije,)536 b(na)510 b(strani)h(16,)536
b(uk)-67 b(azuju)-34 b(\266)-572 b(ci)510 b(na)2435 70411
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%%Page: 15 15
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%%Page: 17 17
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%%Page: 20 20
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%%Page: 21 21
TeXDict begin HPSdict begin 21 20 bop 2435 7181 a FK(Notacija:)837
b FI(f)-202 b(j)202 b FG(:)g(:)g(:)f FI(j)-202 b(g)519
b FO(se)g(k)-34 b(oristi)519 b(za)g(en)-34 b(umeraciju)520
b(k)-34 b(o)34 b(d)519 b(m)-34 b(ultiskup)34 b(o)-34
b(v)-67 b(a,)549 b FI(])519 b FO(ozna)-34 b(\267)-572
b(ca)-34 b(v)-67 b(a)2435 8687 y(uniju)406 b(m)-34 b(ultiskup)34
b(o)-34 b(v)-67 b(a,)404 b(a)g FI(\241)g FO(razliku)f(m)-34
b(ultiskup)34 b(o)-34 b(v)-67 b(a.)4317 11698 y(Pra)-34
b(vila)526 b(prijelaza)g(se)h(k)-34 b(oriste)526 b(za)g(p)34
b(o)-34 b(v)g(eziv)-67 b(anje)527 b(uzastopnih)h(stanja)g(i)e(ostv)-67
b(ari-)2435 13203 y(v)g(anje)355 b(dinamik)-34 b(e)354
b(me)p 12496 12590 364 53 v(du)h(njima.)522 b(Ona)355
b(de\257nira)67 b(ju)356 b FK(prijelaze)385 b(je)-62
b(dno)g(g)386 b(kor)-62 b(aka)p FO(.)520 b(Ak)-34 b(o)354
b(je,)2435 14709 y(na)405 b(primjer,)e(pra)-34 b(vilo)404
b(prijelaza)13811 17410 y FG(F)14590 17592 y FB(1)15117
17410 y FO(\()p FG(x)p FO(\))p FG(;)202 b(F)18070 17592
y FB(1)18596 17410 y FO(\()p FG(x)p FO(\))p FG(;)g(F)21549
17592 y FB(2)22076 17410 y FO(\()p FG(y)43 b FO(\))338
b FI(\241)-202 b(!)336 b FG(G)27235 17592 y FB(1)27761
17410 y FO(\()p FG(x;)202 b(y)43 b FO(\))p FG(;)2435
20111 y FO(tada,)405 b(iz)e(stanja)12226 22812 y FG(S)k
FO(=)337 b FI(f)-202 b(j)p FG(F)16176 22994 y FB(1)16702
22812 y FO(\()p FG(a)p FO(\))p FG(;)202 b(F)19603 22994
y FB(1)20129 22812 y FO(\()p FG(a)p FO(\))p FG(;)g(F)23030
22994 y FB(1)23557 22812 y FO(\()p FG(b)p FO(\))p FG(;)g(F)26337
22994 y FB(2)26864 22812 y FO(\()p FG(a)p FO(\))p FG(;)g(F)29765
22994 y FB(2)30291 22812 y FO(\()p FG(b)p FO(\))p FI(j)-202
b(g)2435 25513 y FO(primjeniv)-64 b(\267)-542 b(si)339
b(gornje)g(pra)-34 b(vilo)339 b(mo)-34 b(\267)-572 b(zemo)339
b(isk)-34 b(oristiti)339 b FG(F)26930 25695 y FB(1)27456
25513 y FO(\()p FG(a)p FO(\))p FG(;)202 b(F)30357 25695
y FB(1)30883 25513 y FO(\()p FG(a)p FO(\))p FG(;)g(F)33784
25695 y FB(2)34311 25513 y FO(\()p FG(b)p FO(\))340 b(i)f(za)f(sljede)
-34 b(\266)-572 b(ce)2435 27018 y(stanje)405 b(dobiti)g
FG(S)10292 26578 y FE(0)10603 27018 y FO(,)14654 28523
y FG(S)15467 28023 y FE(0)16114 28523 y FO(=)337 b FI(f)-202
b(j)p FG(F)18914 28705 y FB(1)19440 28523 y FO(\()p FG(b)p
FO(\))p FG(;)202 b(F)22220 28705 y FB(2)22747 28523 y
FO(\()p FG(a)p FO(\))p FG(;)g(G)25822 28705 y FB(1)26348
28523 y FO(\()p FG(a;)g(b)p FO(\))p FI(j)-202 b(g)p FG(;)2435
30737 y FO(ili)403 b(k)-34 b(oristimo)404 b FG(F)9958
30919 y FB(1)10485 30737 y FO(\()p FG(a)p FO(\))p FG(;)202
b(F)13386 30919 y FB(1)13912 30737 y FO(\()p FG(a)p FO(\))p
FG(;)g(F)16813 30919 y FB(2)17340 30737 y FO(\()p FG(a)p
FO(\))404 b(i)g(dobijamo)h FG(S)26167 30298 y FE(00)26733
30737 y FO(,)14526 33438 y FG(S)15339 32938 y FE(00)16242
33438 y FO(=)336 b FI(f)-202 b(j)p FG(F)19041 33620 y
FB(1)19567 33438 y FO(\()p FG(b)p FO(\))p FG(;)202 b(F)22347
33620 y FB(2)22874 33438 y FO(\()p FG(b)p FO(\))p FG(;)g(G)25828
33620 y FB(1)26355 33438 y FO(\()p FG(a;)g(a)p FO(\))p
FI(j)-202 b(g)p FG(:)2435 36139 y FO(Naprotiv,)404 b(pra)-34
b(vilo)12240 38840 y FG(F)13019 39022 y FB(1)13545 38840
y FO(\()p FG(x)p FO(\))p FG(;)202 b(F)16498 39022 y FB(1)17025
38840 y FO(\()p FG(x)p FO(\))p FG(;)g(F)19978 39022 y
FB(1)20504 38840 y FO(\()p FG(x)p FO(\))p FG(;)g(F)23457
39022 y FB(2)23984 38840 y FO(\()p FG(y)43 b FO(\))338
b FI(\241)-202 b(!)336 b FG(G)29143 39022 y FB(1)29669
38840 y FO(\()p FG(x;)202 b(y)43 b FO(\))2435 41541 y(nije)504
b(mogu)-34 b(\266)-572 b(ce)503 b(primijeniti)g(na)g(stanje)h
FG(S)70 b FO(.)836 b(Stoga,)528 b(da)504 b(bi)f(dobili)470
b(\267)-572 b(cinjenice)502 b(k)-34 b(o)67 b(je)503 b(su)2435
43047 y(instance)389 b(atomarnih)f(form)-34 b(ula)389
b(u)f(k)-34 b(onzekv)g(en)g(ti)388 b(danoga)h(pra)-34
b(vila,)391 b(p)34 b(otrebni)388 b(su)g(nam)2435 44552
y(resursi,)512 b(u)491 b(bro)67 b(ju)492 b(k)-34 b(o)67
b(je)491 b(pra)-34 b(vilo)491 b(zah)-34 b(tjev)-67 b(a.)799
b(T)-101 b(ada)491 b(pra)-34 b(vila)491 b(k)-34 b(onzumira)67
b(ju)492 b(resursne)2402 46058 y(\267)-572 b(cinjenice,)403
b(i)g(o)34 b(d)404 b(njih)h(stv)-67 b(ara)67 b(ju)405
b(no)-34 b(v)g(e.)4317 49069 y(U)404 b(slu)-34 b(\267)-572
b(ca)67 b(ju)405 b(egzistencijalnog)f(kv)-67 b(an)-34
b(ti\257k)-67 b(atora)405 b(u)f(k)-34 b(onzekv)g(en)g(ti,)404
b(na)g(primjer)13027 51770 y FG(F)13806 51952 y FB(1)14332
51770 y FO(\()p FG(x)p FO(\))p FG(;)202 b(F)17285 51952
y FB(1)17812 51770 y FO(\()p FG(x)p FO(\))p FG(;)g(F)20765
51952 y FB(2)21291 51770 y FO(\()p FG(x)p FO(\))338 b
FI(\241)-203 b(!)337 b(9)p FG(y)246 b(G)28019 51952 y
FB(1)28545 51770 y FO(\()p FG(x;)202 b(y)43 b FO(\))p
FG(;)2435 54471 y FO(uv)-34 b(o)34 b(dimo)405 b FK(novi)433
b(konstantni)f(simb)-62 b(ol)p FO(.)537 b(T)-101 b(ada)405
b(se)f FG(S)474 b FO(transformira)405 b(u)14457 57172
y FG(S)15270 56671 y FE(000)16427 57172 y FO(=)337 b
FI(f)-202 b(j)p FG(F)19227 57354 y FB(1)19753 57172 y
FO(\()p FG(b)p FO(\))p FG(;)202 b(F)22533 57354 y FB(2)23060
57172 y FO(\()p FG(b)p FO(\))p FG(;)g(G)26014 57354 y
FB(1)26540 57172 y FO(\()p FG(a;)g(c)p FO(\))p FI(j)-202
b(g)p FG(;)2435 59873 y FO(gdje)382 b(je)g FG(c)f FO(k)-34
b(onstan)g(ta)383 b(o)34 b(dgo)-34 b(v)-67 b(ara)67 b(ju)-34
b(\266)-572 b(ce)382 b(sorte)g(k)-34 b(o)67 b(ja)382
b(se)f(pretho)34 b(dno)383 b(ne)e(p)34 b(o)67 b(ja)-34
b(vljuje)383 b(u)f FG(S)70 b FO(.)2435 61378 y(Isti)412
b(mehanizam)g(funk)-34 b(cionira)412 b(na)g(sin)-34 b(takti)g(\267)-572
b(ck)-34 b(om)412 b(niv)-34 b(ou,)414 b(k)-34 b(o)34
b(d)412 b(priro)34 b(dne)412 b(deduk)-34 b(cije,)2435
62884 y(pri)404 b(eliminaciji)f(egzistencijalnog)h(kv)-67
b(an)-34 b(ti\257k)-67 b(atora.)4317 65894 y(Izrazimo)422
b(precizno)358 b(\267)-542 b(sto)423 b(zna)-34 b(\267)-572
b(ci)423 b(primjeniti)g(pra)-34 b(vilo)422 b(na)h(stanje.)596
b FK(Supstitucija)512 b FO(je)2435 67400 y(funk)-34 b(cija)527
b(k)-34 b(o)67 b(ja)527 b(v)-67 b(arijablama)526 b(pridru)-34
b(\267)-572 b(zuje)526 b(terme)g(o)34 b(dgo)-34 b(v)-67
b(ara)67 b(ju)-34 b(\266)-572 b(ce)526 b(sorte.)904 b(Supstitu-)2435
68905 y(cija)524 b(je)g FK(p)-62 b(otpuna)615 b FO(za)523
b(neku)i(form)-34 b(ulu)525 b(ak)-34 b(o)524 b(preslik)-67
b(a)-34 b(v)-67 b(a)522 b(sv)-34 b(e)524 b(v)-67 b(arijable)523
b(te)h(form)-34 b(ule)524 b(u)2435 70411 y(adekv)-67
b(atne)411 b(terme.)559 b(Re)-34 b(\266)-572 b(ci)377
b(\266)-572 b(cemo)411 b(da)g(supstitucija)i FG(\276)26864
69971 y FE(0)27586 70411 y FK(pr)-62 b(o)g(\267)-558
b(siruje)499 b FO(supstituciju)414 b FG(\276)454 b FO(ak)-34
b(o)2435 71916 y FG(\276)380 b FI(\275)337 b FG(\276)5524
71476 y FE(0)5834 71916 y FO(.)539 b(Pri)403 b(tom)i(je)f
FG(\276)13291 71476 y FE(0)13938 71916 y FO(=)337 b FG(\276)312
b FI([)270 b(f)p FG(x)18600 72098 y FB(1)19462 71916
y FI(7!)337 b FG(t)21449 72098 y FB(1)21974 71916 y FG(;)202
b(x)23206 72098 y FB(2)24068 71916 y FI(7!)337 b FG(t)26055
72098 y FB(2)26581 71916 y FG(;)202 b(:)g(:)g(:)e(;)i(x)29967
72098 y FF(n)30930 71916 y FI(7!)337 b FG(t)32917 72098
y FF(n)33543 71916 y FI(g)p FO(.)21755 74956 y(21)p eop
end end
%%Page: 22 22
TeXDict begin HPSdict begin 22 21 bop 7749 7181 a FL(De\257nicija)465
b(4)606 b FK(Pr)-62 b(avilo)18870 9931 y FG(F)19649 10113
y FB(1)20175 9931 y FG(;)202 b(F)21493 10113 y FB(2)22019
9931 y FG(;)g(:::;)g(F)24887 10128 y FF(k)25792 9931
y FI(\241)-203 b(!)337 b(9)-10 b FG(~)-596 b(y)246 b(G)30547
10113 y FB(1)31073 9931 y FG(;)202 b(G)32565 10113 y
FB(2)33091 9931 y FG(;)g(:::;)g(G)36133 10128 y FF(l)7749
12681 y FK(je)540 b FO(primjenjiv)-34 b(o)451 b FK(na)g(stanje)e
FG(S)520 b FK(ako)449 b(p)-62 b(ostoji)448 b(p)-62 b(otpuna)448
b(supstitucija)d FG(\276)494 b FK(za)449 b(to)h(pr)-62
b(avilo,)7749 14187 y(i)495 b(stanje)e FG(S)12982 14369
y FB(0)14003 14187 y FK(takvo)g(da)i FG(S)518 b FO(=)448
b FG(S)22385 14369 y FB(0)23225 14187 y FI(])313 b(f)-202
b(j)p FG(\276)43 b(F)26602 14369 y FB(1)27129 14187 y
FG(;)202 b(\276)43 b(F)29183 14369 y FB(2)29709 14187
y FG(;)202 b(:::;)g(\276)43 b(F)33313 14384 y FF(k)33881
14187 y FI(j)-202 b(g)p FK(.)741 b(R)-62 b(ezultir)g(aju)-31
b(\266)-589 b(ce)491 b(stanje)j(je)7749 15692 y(tada)18964
17224 y FG(S)19777 16724 y FE(0)20425 17224 y FO(=)336
b FG(S)22447 17406 y FB(0)23242 17224 y FI(])270 b(f)-202
b(j)p FG(\276)25797 16724 y FE(0)26107 17224 y FG(G)27060
17406 y FB(1)27586 17224 y FG(;)202 b(\276)28861 16724
y FE(0)29171 17224 y FG(G)30124 17406 y FB(2)30650 17224
y FG(;)g(:::;)g(\276)33475 16724 y FE(0)33785 17224 y
FG(G)34738 17421 y FF(k)35306 17224 y FI(j)-202 b(g)p
FG(;)7749 19481 y FK(a)580 b(supstitucija)575 b FG(\276)16274
19041 y FE(0)17165 19481 y FK(pr)-62 b(o)g(\267)-558
b(siruje)578 b FG(\276)623 b FK(pr)-62 b(eslikavaju)-31
b(\266)-589 b(ci)566 b FG(~)-596 b(y)624 b FK(varijable)577
b(u)j(nove)g(konstantne)7749 20986 y(simb)-62 b(ole)365
b FG(~)-540 b(c)p FK(.)7749 23865 y FL(De\257nicija)465
b(5)606 b FK(Neka)308 b(je)h FG(F)479 b FK(r)-62 b(elacijski)306
b(simb)-62 b(ol.)515 b(Ka)-62 b(\267)-558 b(zemo)308
b(da)h(pr)-62 b(avilo)307 b(prijelaza)400 b FO(k)-34
b(onzu-)7749 25370 y(mira)407 b(F-)-34 b(\267)-572 b(cinjenice)438
b FK(ako)e(se)g(neka)h(atomarna)f(formula)g FG(F)168
b FO(\()-16 b FG(~)-590 b(x)q FO(\))438 b FK(p)-62 b(ojavljuje)433
b(vi)-62 b(\267)-558 b(se)436 b(puta)g(u)7749 26876 y(ante)-62
b(c)g(e)g(denti,)444 b(ne)-62 b(go)444 b(u)g(konzekventi)e(to)-62
b(ga)443 b(pr)-62 b(avila.)587 b(Pr)-62 b(avilo)520 b
FO(kreira)414 b(F-)-34 b(\267)-572 b(cinjenice)445 b
FK(ako)7749 28381 y(se)313 b(neka)g FG(F)168 b FO(\()-16
b FG(~)-590 b(x)q FO(\))314 b FK(p)-62 b(ojavljuje)310
b(manje)k(puta)e(u)h(ante)-62 b(c)g(e)g(denti)312 b(ne)-62
b(go)313 b(u)g(konzekventi.)515 b(Pr)-62 b(avilo)7715
29887 y FO(\267)-572 b(cuv)-67 b(a)328 b(F-)-34 b(\267)-572
b(cinjenice)363 b FK(ako)g(se)g(svaka)f FG(F)168 b FO(\()-16
b FG(~)-590 b(x)q FO(\))364 b FK(p)-62 b(ojavljuje)360
b(je)-62 b(dnaki)362 b(br)-62 b(oj)363 b(puta)f(u)i(ante)-62
b(c)g(e)g(denti)7749 31392 y(kao)432 b(u)h(konzekventi.)9631
34271 y FO(Nek)-67 b(a)403 b(je)h FG(S)j FO(=)336 b FI(f)-202
b(j)p FG(F)168 b FO(\()p FG(a)p FO(\))p FG(;)202 b(G)p
FO(\()p FG(b)p FO(\))p FI(j)-202 b(g)p FO(,)406 b(tada)e(pra)-34
b(vilo)23775 37021 y FG(F)168 b FO(\()p FG(x)p FO(\))338
b FI(\241)-202 b(!)337 b FG(G)p FO(\()p FG(x)p FO(\))7749
39771 y(kreira)470 b FG(G)p FO(-)-34 b(\267)-572 b(cinjenice)470
b(i)h(k)-34 b(onzumira)472 b FG(F)168 b FO(-)-34 b(\267)-572
b(cinjenice,)488 b(i)470 b(rezultan)-34 b(tno)473 b(stanje)f
FG(S)42922 39331 y FE(0)43704 39771 y FO(je)f FG(S)45897
39331 y FE(0)46657 39771 y FO(=)7749 41276 y FI(f)-202
b(j)p FG(G)p FO(\()p FG(a)p FO(\))p FG(;)202 b(G)p FO(\()p
FG(b)p FO(\))p FI(j)-202 b(g)p FO(.)539 b(Pra)-34 b(vilo)22241
42808 y FG(F)168 b FO(\()p FG(x)p FO(\))p FG(;)202 b(G)p
FO(\()p FG(y)43 b FO(\))340 b FI(\241)-203 b(!)337 b
FG(F)168 b FO(\()p FG(x)p FO(\))7715 45065 y(\267)-572
b(cuv)-67 b(a)269 b FG(F)168 b FO(-)-34 b(\267)-572 b(cinjenice)269
b(i)g(k)-34 b(onzumira)270 b FG(G)p FO(-)-34 b(\267)-572
b(cinjenice,)296 b(no)-34 b(v)g(o)34 b(dobiv)-34 b(eno)270
b(stanje)h(je)e FG(S)42385 44625 y FE(0)43033 45065 y
FO(=)336 b FI(f)-202 b(j)p FG(F)168 b FO(\()p FG(a)p
FO(\))p FI(j)-202 b(g)p FO(.)7749 46570 y(Uo)-34 b(\267)-572
b(cimo)453 b(da)g(pra)-34 b(vilo)453 b FG(F)168 b FO(\()-16
b FG(~)-590 b(x)q FO(\))419 b FI(\241)-202 b(!)419 b
FG(F)168 b FO(\()-10 b FG(~)-596 b(y)45 b FO(\))453 b(niti)420
b(\267)-572 b(cuv)-67 b(a,)464 b(niti)454 b(kreira,)464
b(niti)453 b(k)-34 b(onzumira)453 b FG(F)168 b FO(-)7715
48076 y(\267)-572 b(cinjenice.)538 b(Primjenjeno)404
b(na)h FG(S)474 b FO(da)67 b(je)405 b FG(S)26365 47636
y FE(0)27012 48076 y FO(=)337 b FI(f)-202 b(j)p FG(F)168
b FO(\()p FG(c)p FO(\))p FG(;)202 b(G)p FO(\()p FG(b)p
FO(\))p FI(j)-202 b(g)p FO(.)7749 50963 y FL(De\257nicija)465
b(6)606 b FK(Pr)-62 b(e)g(dikat)593 b FG(F)764 b FK(je)686
b FO(p)34 b(erzisten)-34 b(tan)596 b FK(za)f(te)-62 b(oriju)593
b(tr)-62 b(ansformacija)593 b(multi-)7749 52469 y(skup)-62
b(ova)430 b FI(T)742 b FK(ako)432 b(sva)h(pr)-62 b(avila)431
b(iz)i FI(T)711 b FK(\267)-589 b(cuvaju)431 b FG(F)168
b FK(-)-31 b(\267)-589 b(cinjenic)-62 b(e.)9631 55347
y FO(In)-34 b(tuitivno)317 b(se)f(tranzicije)g(mogu)h(promatrati)g(k)
-67 b(ao)316 b(k)-34 b(emijsk)g(e)316 b(reak)-34 b(cije:)494
b(na)317 b(lijev)-34 b(o)67 b(j)7749 56853 y(strani)537
b(pra)-34 b(vila)536 b(imamo)h(molekule)f(k)-34 b(o)67
b(je)537 b(sudjeluju)h(u)f(reak)-34 b(ciji,)569 b(na)537
b(desno)67 b(j)538 b(strani)7749 58358 y(se)403 b(p)34
b(o)67 b(ja)-34 b(vljuju)407 b(one)d(no)-34 b(v)g(onastale.)539
b(Uk)-34 b(olik)g(o)404 b(mo)-34 b(\267)-572 b(zemo)404
b(primijeniti)f(dano)i(pra)-34 b(vilo)404 b(na)7749 59864
y(m)-34 b(ultiskup)307 b FG(S)70 b FO(,)326 b(p)34 b(o)-34
b(\267)-572 b(cetn)-34 b(u)307 b(soluciju,)326 b(reak)-34
b(cijom)306 b(dobijamo)h(no)-34 b(vu)308 b(soluciju,)325
b FG(S)42883 59424 y FE(0)43194 59864 y FO(.)506 b(P)-34
b(erzis-)7749 61369 y(ten)g(tne)405 b(p)34 b(o)g(datk)-34
b(e,)404 b(mo)-34 b(\267)-572 b(zemo)404 b(zami)-64 b(\267)-542
b(sljati)404 b(k)-67 b(ao)404 b(k)-67 b(atalizatore.)7749
62875 y(Kemijsk)g(a)540 b(metafora)h(je)g(dublje)h(razra)p
26587 62261 364 53 v(dena)e(u)h(\([BB92]\),)575 b(gdje)541
b(k)-34 b(emijski)540 b(stro)67 b(jevi)7749 64380 y(\()p
FK(chams)99 b FO(\))431 b(mo)34 b(delira)67 b(ju)431
b(paralelne)g(pro)34 b(cese.)619 b(T)-101 b(amo)432 b(su)g(reak)-34
b(cije)430 b(tak)-34 b(o)p 40722 63766 V(der)432 b(prik)-67
b(azane)7749 65886 y(u)404 b(formi)g(transformacija)h(m)-34
b(ultiskup)34 b(o)-34 b(v)-67 b(a.)9631 68905 y(U)359
b(jeziku)f(sigurnosnih)i(protok)-34 b(ola,)369 b(primjeri)358
b(ak)-34 b(cija)359 b(k)-34 b(o)67 b(je)360 b(opisujemo)g(pra)-34
b(vilima)7749 70411 y(prijelaza)357 b(su)g(slanje)h(i)f(primanje)h(p)34
b(oruk)-34 b(e.)523 b(P)-34 b(erzisten)g(tna)325 b(\267)-572
b(cinjenica)356 b(mo)-34 b(\267)-572 b(ze)357 b(biti)h(agen-)7749
71916 y(to)-34 b(v)353 b(ja)-34 b(vni)354 b(klju)-34
b(\267)-572 b(c,)362 b(p)34 b(oznat)354 b(je)f(svima,)362
b(sv)-67 b(atk)-34 b(o)353 b(ga)g(mo)-34 b(\267)-572
b(ze)353 b(k)-34 b(oristiti)353 b(te)g(je)319 b(\267)-572
b(cinjenica)352 b(k)-34 b(o)67 b(ja)27068 74956 y(22)p
eop end end
%%Page: 23 23
TeXDict begin HPSdict begin 23 22 bop 2435 7181 a FO(se)347
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b(ji)405 b(nosi)g(informaciju)g(o)g(bro)67 b(ju)406 b(usp)67
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10192 y(agen)-34 b(ta)466 b(u)f(sesiji)f(protok)-34 b(ola,)480
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b(a)404 b(u)g(sesiji.)4317 14803 y(Ov)-67 b(a)297 b(notaciju)i(je)e
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b(ci)269 b(na)i([slides)o(].)494 b(Dalje)269 b(je)i(razra)p
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b(clanku)337 b(Cerv)-34 b(esato,)351 b(Durgin,)f(Lincoln,)g(Mitc)-34
b(hell,)351 b(Scedro)-34 b(v:)505 b([CDL)34969 17374
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b(vljenja)407 b(preuzeti)c(iz)h([CDL)26557 20385 y FB(+)27344
20825 y FO(00].)2435 25184 y FH(3.2)1793 b(Opis)598 b(protok)-50
b(ola)2435 28073 y FL(Rje)-39 b(\267)-658 b(cnik)361
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b(\267)-572 b(c;)460 b(sorta)442 b(soli)g(je)2435 32590
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b(o)g(dacima)353 b(mo)-34 b(\267)-572 b(ze)353 b(biti)h(slabije,)363
b(zato)320 b(\266)-572 b(cemo)353 b(nek)-34 b(e)353 b(ok)-67
b(arakter-)2435 34095 y(izirati)467 b(op)-34 b(\266)-572
b(com)468 b(sortom)f(za)h(p)34 b(oruk)-34 b(e)467 b FN(msg)p
FO(.)728 b(Sorte)468 b(se)f(preklapa)67 b(ju,)484 b(relacija)467
b(ure)p 40224 33481 364 53 v(da)67 b(ja)2435 35601 y(na)418
b(njima)g(je)f(standardna)i(inkluzija:)565 b FN(nonce)p
FO(,)420 b FN(cipher)p FO(,)p FN(e)p 28315 35601 364
45 v 436 w(k)-34 b(ey)16 b FO(,)420 b FN(d)p 31807 35601
V 437 w(k)-34 b(ey)375 b FI(\265)417 b FN(msg)p FO(.)577
b(Un)-34 b(utar)2435 37106 y(o)g(v)g(og)298 b(okvira)d(nema)i(sp)34
b(ecijalne)296 b(sorte)h(za)g(imena)f(agenata,)319 b(njih)297
b(se)g(iden)-34 b(ti\257cira)297 b(prek)-34 b(o)2435
38612 y(ja)g(vnih)405 b(klju)-34 b(\267)-572 b(cev)-67
b(a.)2435 40117 y(Signatura)380 b(se)e(sv)-67 b(ak)g(ak)-34
b(o)377 b(mo)-34 b(\267)-572 b(ze)378 b(prilago)34 b(ditii)377
b(za)h(p)34 b(otreb)g(e)378 b(simetri)-34 b(\267)-572
b(cne)377 b(enkrip)34 b(cije,)382 b(a)c(u)2435 41622
y(tom)405 b(se)f(slu)-34 b(\267)-572 b(ca)67 b(ju)405
b(sorte)f FN(e)p 14081 41622 V 436 w(k)-34 b(ey)421 b
FO(i)403 b FN(d)p 17961 41622 V 437 w(k)-34 b(ey)420
b FO(p)34 b(o)g(dudara)67 b(ju.)4317 44728 y FL(Predik)-77
b(ati)350 b FO(uklju)-34 b(\267)-572 b(cuju)352 b(relacijski)c(sim)-34
b(b)34 b(ol)351 b FN(N)e FO(k)-34 b(o)67 b(ji)351 b(mo)34
b(delira)349 b(mre)-34 b(\267)-572 b(zu.)521 b(Argumen)-34
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b(o)34 b(dzivnik,)539 b(imamo)513 b(skup)g(predik)-67
b(ata)513 b(role)f FI(f)p FN(A)25048 49433 y FF(\275)p
Fz(i)26012 49244 y FI(j)202 b FG(i)518 b FO(=)f(0)202
b FG(:)g(:)g(:)g(k)38 b FI(g)p FO(,)540 b(k)-34 b(o)67
b(ji)513 b(obilje)-34 b(\267)-572 b(za)-34 b(v)-67 b(a)67
b(ju)2435 50750 y(k)-34 b(orak)g(e)404 b(izvr)-64 b(\267)-542
b(senja)404 b(protok)-34 b(ola.)539 b(Ti)404 b(predik)-67
b(ati)403 b(o)-34 b(vise)404 b(o)g(p)34 b(o)67 b(jedinom)405
b(protok)-34 b(olu.)2435 52255 y(Drugi)419 b(predik)-67
b(ati)418 b(ozna)-34 b(\267)-572 b(ca)-34 b(v)-67 b(a)67
b(ju)420 b(stati)-34 b(\267)-572 b(ck)-34 b(e)419 b(elemen)-34
b(te)419 b(protok)-34 b(ola,)422 b(k)-67 b(ao)355 b(\267)-542
b(sto)419 b(je)g FN(KeyP)-34 b(air)17 b FO(,)2402 53761
y(\267)-572 b(ciji)434 b(je)i(prvi)e(argumen)-34 b(t)437
b(sorte)e FN(e)p 17429 53761 V 436 w(k)-34 b(ey)17 b
FO(,)443 b(a)435 b(drugi)h(sorte)f FN(d)p 28190 53761
V 437 w(k)-34 b(ey)16 b FO(,)443 b(i)435 b(ciljana)g(je)h(seman)-34
b(tik)-67 b(a)2435 55266 y(p)34 b(o)-34 b(v)g(eziv)-67
b(anje)496 b(ja)-34 b(vnog)497 b(klju)-34 b(\267)-572
b(ca)496 b(s)h(njego)-34 b(vim)496 b(priv)-67 b(atnim)496
b(in)-34 b(v)g(erzom.)815 b(Predik)-67 b(at)496 b FN(AnnK)2435
56772 y FO(ozna)-34 b(\267)-572 b(ca)-34 b(v)-67 b(a)404
b(ogla)-64 b(\267)-542 b(seni)404 b(ja)-34 b(vni)405
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b(te)658 b(se)d(mogu)h(smatrati)h(n)-34 b(ularnim)656
b(funk)-34 b(cijama,)720 b(a)656 b(nen)-34 b(ularne)656
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b(spariv)-67 b(anje)540 b(ili)f(k)-34 b(onk)-67 b(atenacija,)573
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b FI(\241)-202 b(!)538 b FN(msg)17 b FO(,)573 b(i)2435
61288 y(enkrip)34 b(cija,)403 b FN(enc)539 b FO(:)f FN(e)p
12128 61288 V 436 w(k)-34 b(ey)286 b FI(\243)269 b FN(msg)353
b FI(\241)-202 b(!)337 b FN(cipher)16 b FO(.)4317 64393
y(Dekrip)34 b(cija)420 b(se)h(ne)g(mo)34 b(delira)420
b(p)34 b(osebnim)422 b(funk)-34 b(cijskim)422 b(sim)-34
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b(omo)-34 b(\266)-572 b(cu)2435 65899 y(p)34 b(oklapanja)426
b(uzorak)-67 b(a)424 b(\()p FK(p)-62 b(attern)451 b(matching)107
b FO(\))424 b(s)g(enkrip)34 b(cijom)424 b(u)h(an)-34
b(teceden)g(ti.)601 b(Prim-)2435 67404 y(jer)465 b(mo)-34
b(\267)-572 b(ze)463 b(biti)i(pra)-34 b(vilo)464 b(A2,)479
b(u)465 b(daljnjem)h(tekstu)f(sp)34 b(eci\257ciranog)464
b(\(3.3\))g(Dolev{Y)-101 b(ao)2435 68910 y(protok)-34
b(ola)405 b(ja)-34 b(vnog)405 b(klju)-34 b(\267)-572
b(ca,)404 b(skiciranog)f(na)i(slici)e(2.4.)7763 71916
y FN(A)8571 72098 y Fz(1)9097 71916 y FO(\()p FG(k)10199
72098 y FF(e)10691 71916 y FG(;)202 b(k)11899 71416 y
FE(0)11861 72216 y FF(e)12353 71916 y FG(;)g(x)p FO(\))p
FG(;)403 b FN(N)p FO(\()p FN(enc)p FO(\()p FG(k)18932
72098 y FF(e)19424 71916 y FG(;)202 b FI(h)p FN(enc)p
FO(\()p FG(k)23240 72098 y FF(e)23732 71916 y FG(;)g(x)p
FO(\))p FG(;)g(k)26643 71416 y FE(0)26605 72216 y FF(e)27097
71916 y FI(i)p FO(\))337 b FI(\241)-202 b(!)337 b FN(A)31474
72098 y Fz(2)32000 71916 y FO(\()p FG(k)33102 72098 y
FF(e)33594 71916 y FG(;)202 b(k)34802 71416 y FE(0)34764
72216 y FF(e)35255 71916 y FG(;)g(x)p FO(\))21755 74956
y(23)p eop end end
%%Page: 24 24
TeXDict begin HPSdict begin 24 23 bop 7749 7181 a FO(Pra)-34
b(vilo)291 b(opisuje)h(inicijatoro)-34 b(v)g(o)292 b(primanje)g(druge)g
(p)34 b(oruk)-34 b(e)291 b(protok)-34 b(ola.)502 b(Inicijator)291
b(je)h(u)7749 8687 y(stanju)321 b FN(A)12149 8869 y Fz(1)12675
8687 y FO(,)337 b(zna)320 b(vlastiti)g(ja)-34 b(vni)321
b(klju)-34 b(\267)-572 b(c)320 b FG(k)25907 8869 y FF(e)26398
8687 y FO(,)337 b(o)34 b(dzivnik)-34 b(o)g(v)320 b(ja)-34
b(vni)320 b(klju)-34 b(\267)-572 b(c)320 b FG(k)39509
8247 y FE(0)39471 8986 y FF(e)39963 8687 y FO(,)336 b(i)320
b(sol)g FG(x)g FO(k)-34 b(o)67 b(ju)321 b(je)7749 10192
y(kreirao)401 b(pretho)34 b(dno)404 b(u)f(protok)-34
b(olu.)539 b(T)-101 b(ak)-34 b(o)p 27513 9579 364 53
v(der,)403 b(inicijator)f(je)h(inicijaliziran)e(s)i(ob)67
b(ja)-34 b(vl-)7749 11698 y(jenim)407 b(ja)-34 b(vnim)408
b(klju)-34 b(\267)-572 b(cem)406 b(\(za)h(to)h(treba)f(vidjeti)g
(inicijalizacijsku)f(fazu,)h(strana)h(26\))g(i)7749 13203
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b(\267)-572 b(ca.)528 b(Na)371 b(ta)67 b(j)372 b(na)-34
b(\267)-572 b(cin)372 b(otv)-67 b(ara)371 b(p)34 b(oslan)-34
b(u)372 b(enkrip)34 b(ciju,)7749 14709 y(argumen)-34
b(t)430 b(predik)-67 b(ata)429 b FN(N)f FO(u)i(an)-34
b(teceden)g(ti,)436 b(k)-34 b(o)67 b(ju)430 b(m)-34 b(u)430
b(je)f(o)34 b(dzivnik)428 b(p)34 b(oslao.)613 b(Predik)-67
b(at)7749 16214 y FN(A)8557 16396 y Fz(2)9500 16214 y
FO(u)419 b(k)-34 b(onzekv)g(en)g(ti)418 b(zna)-34 b(\267)-572
b(ci)417 b(da)i(je)f(inicijator)f(pro)-34 b(\267)-572
b(citao)418 b(tu)h(p)34 b(oruku,)422 b(i)417 b(p)34 b(ostigao)419
b(cilj)e(u)7749 17720 y(to)67 b(j)349 b(rundi)g(protok)-34
b(ola,)360 b(na)-64 b(\267)-542 b(sa)-34 b(v)-64 b(\267)-542
b(si)348 b(sol)g FG(x)g FO(i)g(o)34 b(dzivnik)-34 b(o)g(v)g(o)348
b(ime)g FG(k)35582 17280 y FE(0)35544 18019 y FF(e)36384
17720 y FO(kriptirano)g(s)h(njego)-34 b(vim)7749 19225
y(ja)g(vnim)404 b(klju)-34 b(\267)-572 b(cem)404 b FG(k)16898
19407 y FF(e)17390 19225 y FO(.)9631 22236 y(Pra)-34
b(vila)285 b(prijelaza)g(mora)67 b(ju)287 b(izraziti)e(sv)-34
b(e)286 b(ak)-34 b(cije)285 b(u)i(protok)-34 b(olu.)500
b(T)-101 b(e)286 b(osno)-34 b(vne)287 b(ak)-34 b(cije)7749
23741 y(su)288 b FK(slanje)378 b FO(p)34 b(oruk)-34 b(e)288
b(i)g FK(primanje)378 b FO(p)34 b(oruk)-34 b(e.)500 b(P)-34
b(osebno)289 b(pra)-34 b(vilo)288 b(je)g FK(pr)-62 b(avilo)325
b(kr)-62 b(eir)g(anja)326 b(r)-62 b(ole)p FO(,)7749 25247
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b(za)g(p)34 b(o)-34 b(\267)-572 b(cetno)404 b(stv)-67
b(aranje)405 b(role)e FG(\275)h FO(za)f(p)34 b(o)67 b(jedinog)406
b(aktera)d(protok)-34 b(ola.)7749 26752 y FL(Pra)-39
b(vilo)464 b(kreiranja)g(role)404 b FO(je)h(oblik)-67
b(a:)21996 29385 y FG(\274)43 b FO(\()-16 b FG(~)-590
b(x)p FO(\))338 b FI(\241)-203 b(!)337 b FN(A)27800 29567
y FF(\275)p Fz(0)28808 29385 y FO(\()-16 b FG(~)-590
b(x)p FO(\))p FG(;)202 b(\274)43 b FO(\()-16 b FG(~)-590
b(x)q FO(\))7749 32018 y(Predik)-67 b(at)359 b FG(\274)404
b FO(ob)67 b(jedinjuje)362 b(sv)-34 b(e)360 b(p)34 b(ezisten)-34
b(tne)361 b(p)34 b(o)g(datk)-34 b(e)360 b(prisutne)h(un)-34
b(utar)362 b(pra)-34 b(vila)360 b(\(o)34 b(d-)7749 33523
y(nosno,)369 b(un)-34 b(utar)362 b(teorije\).)524 b(Argumen)-34
b(t)344 b FG(~)-589 b(x)359 b FO(ozna)-34 b(\267)-572
b(ca)-34 b(v)-67 b(a)360 b(v)-67 b(arijable)359 b FG(x)37436
33705 y FB(1)37962 33523 y FG(;)202 b(x)39194 33705 y
FB(2)39719 33523 y FG(;)g(:)g(:)g(:)f(;)h(x)43106 33720
y FF(k)44034 33523 y FO(k)-34 b(o)67 b(je)360 b(se)7749
35029 y(ne)404 b(p)34 b(o)67 b(ja)-34 b(vljuju)406 b(n)-34
b(u)g(\267)-572 b(zno)405 b(sv)-34 b(e)404 b(un)-34 b(utar)406
b(dane)f(atomarne)f(form)-34 b(ule.)9631 38040 y FL(Slanje)404
b FO(se)g(prik)-67 b(azuje)403 b(k)-67 b(ao:)13978 40673
y FN(A)14786 40862 y FF(\275)p Fz(i)15548 40673 y FO(\()-16
b FG(~)-590 b(x)p FO(\))p FG(;)202 b(\274)43 b FO(\()-20
b FG(~)-586 b(z)54 b FO(\))337 b FI(\241)-202 b(!)337
b(9)-32 b FG(~)-574 b(n)202 b FN(A)25054 40862 y FF(\275)p
Fz(i)p FB(+)p Fz(1)27018 40673 y FO(\()-16 b FG(~)-590
b(x;)182 b(~)-586 b(z)52 b(;)170 b(~)-574 b(n)p FO(\))p
FG(;)202 b FN(N)p FO(\()p FG(m)p FO(\()-16 b FG(~)-590
b(x;)182 b(~)-586 b(z)53 b(;)170 b(~)-574 b(n)o FO(\)\))p
FG(;)202 b(\274)43 b FO(\()-20 b FG(~)-586 b(z)54 b FO(\))7749
43305 y(gdje)343 b(egzistencijalni)f(kv)-67 b(an)-34
b(ti\257k)-67 b(ator)343 b(na)h(desno)67 b(j)344 b(strani)f(tranzicije)
g(o)34 b(dra)-34 b(\267)-572 b(za)-34 b(v)-67 b(a)342
b(generi-)7749 44811 y(ranje)298 b(no)-34 b(v)g(e)298
b(vrijednosti,)319 b(tipi)-34 b(\267)-572 b(cno)298 b(soli,)318
b(k)-34 b(o)67 b(ja)299 b(se)e(tada)i(k)-34 b(omp)34
b(onira)298 b(u)g(p)34 b(oruku)298 b(i)g(sta)-34 b(vlja)7749
46316 y(na)362 b(mre)-34 b(\267)-572 b(zu.)524 b(Argumen)-34
b(t)364 b FG(m)e FO(predik)-67 b(ata)362 b FN(N)f FO(ozna)-34
b(\267)-572 b(ca)-34 b(v)-67 b(a)362 b(bilo)g(k)-34 b(o)67
b(ji)363 b FN(msg)378 b FO(term)362 b(k)-34 b(o)67 b(ji)363
b(sadr)-34 b(\267)-572 b(zi)7749 47822 y(nek)-34 b(e)404
b(o)34 b(d)404 b(na)-34 b(v)g(edenih)405 b(v)-67 b(arijabli.)9631
50833 y FL(Primanje)403 b FO(je)h(jednosta)-34 b(vno:)15895
53466 y FN(A)16703 53655 y FF(\275)p Fz(i)17464 53466
y FO(\()-16 b FG(~)-590 b(x)q FO(\))p FG(;)202 b FN(N)p
FO(\()p FG(m)p FO(\()-10 b FG(~)-596 b(y)44 b FO(\)\))p
FG(;)202 b(\274)43 b FO(\()-20 b FG(~)-586 b(z)54 b FO(\))337
b FI(\241)-202 b(!)337 b FN(A)30352 53655 y FF(\275)p
Fz(i)p FB(+)p Fz(1)32316 53466 y FO(\()-16 b FG(~)-590
b(x;)192 b(~)-596 b(y)44 b(;)182 b(~)-586 b(z)52 b FO(\))p
FG(;)202 b(\274)43 b FO(\()-20 b FG(~)-586 b(z)54 b FO(\))p
FG(:)7749 56098 y FO(Kom)-34 b(biniranjem)470 b(o)-34
b(v)-67 b(a)470 b(dv)-67 b(a)469 b(pra)-34 b(vila,)486
b(primanje)470 b(i)f(slanje)h(mogu)g(biti)g(prik)-67
b(azani)469 b(k)-67 b(ao)7749 57604 y(jedan)405 b(k)-34
b(orak)403 b(izvr)-64 b(\267)-542 b(senja)404 b(protok)-34
b(ola)405 b(nek)-34 b(og)404 b(agen)-34 b(ta.)9631 60615
y(Protok)g(olsk)-67 b(a)403 b(teorija)h(transformacija)h(m)-34
b(ultiskup)34 b(o)-34 b(v)-67 b(a)405 b(sasto)67 b(ji)405
b(se)f(o)34 b(d)404 b(tri)g(faze:)9567 63041 y FI(\262)606
b FO(inicijalizacijsk)-34 b(e)403 b(faze,)9567 65513
y FI(\262)606 b FO(faze)404 b(kreiranja)g(roli,)e(i)9567
67984 y FI(\262)606 b FO(faze)404 b(opisa)g(protok)-34
b(ola)405 b(\(roli\).)9631 70411 y(U)434 b FK(inicijalizacijskoj)456
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b(o)67 b(jstv)-67 b(a)435 b(i)f(relacije)f(me)p 40759
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y(24)p eop end end
%%Page: 25 25
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v(der,)571 b(istakn)-34 b(ute)540 b(su)e(plauzi-)2435
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b(at)309 b(role)f(\(na)i(strani)g(24\).)507 b(Drugi)2435
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35788 y(jedino)67 b(j)515 b(roli)d(o)34 b(dre)p 11439
35175 V(denog)513 b(protok)-34 b(ola.)866 b(Pra)-34 b(vila)512
b(k)-34 b(o)67 b(ja)514 b(opisuju)h(ak)-34 b(cije)512
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%%Page: 26 26
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%%Page: 27 27
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%%Page: 28 28
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52805 y(bro)67 b(j)405 b(instanci)f(rola)g(i)g(sl.)7749
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b FN(I)p FO(\()p FG(X)95 b FO(\),)404 b(gdje)h(je)f FG(X)500
b FO(p)34 b(oruk)-67 b(a)403 b(za)h(k)-34 b(o)67 b(ju)405
b(se)f(smatralo)h(da)f(je)g FK(tajna)p FO(.)9631 58827
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b(cku)412 b(situaciju,)381 b(\267)-572 b(cime)378 b(\266)-572
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60332 y(zo)-34 b(v)g(e)404 b(sp)34 b(osobnosti.)7749
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b(\267)-589 b(cava)431 b FI(j)p FG(f)130 b FI(j)434 b
FK(i)f(de\257nir)-62 b(a)434 b(induktivno:)9567 65477
y FI(\262)606 b(j)p FG(x)p FI(j)422 b FO(=)g(1)p FK(,)492
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FG(c)p FI(j)421 b FO(=)h(1)481 b FK(za)f(konstantu)f
FG(c)i FK(sorti)e Fq(nonce)p FK(,)493 b FN(e)p 44020
65477 372 45 v 446 w(k)-34 b(ey)497 b FK(ili)10779 66982
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69449 y FI(\262)606 b(j)p FG(P)168 b FO(\()p FG(m)p FO(\))p
FI(j)338 b FO(=)e FI(j)p FG(m)p FI(j)269 b FO(+)g(1)p
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b(j)p FG(P)438 b FI(^)269 b FG(Q)p FI(j)337 b FO(=)f
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FO(+)g(1)27068 74956 y(28)p eop end end
%%Page: 29 29
TeXDict begin HPSdict begin 29 28 bop 4253 7181 a FI(\262)607
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FI(\241)-203 b(!)337 b FG(Q)p FI(j)g FO(=)f FI(j)p FG(P)168
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14759 y(Jednosta)-34 b(vno,)623 b(duljin)-34 b(u)580
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b(9)606 b FO(V)-101 b(eli)-34 b(\267)-572 b(cina)320
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b(form)-34 b(uliran,)297 b(za)67 b(jedno)272 b(s)e(dok)-67
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b(\267)-572 b(cno)396 b(su)g(napra)-34 b(vili)396 b(R.)g(Amadio,)h(D.)f
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b(cols\).)721 b(Pretho)34 b(dno)465 b(su)g(u)h([AF01])e(Abadi)i(i)e
(Fiore)h(bili)f(blizu)2435 31935 y(dok)-67 b(aza)358
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y(dotakli)404 b(pitanja)i(slo)-34 b(\267)-572 b(zenosti.)2435
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b(a)571 b(pr)-62 b(otokolske)569 b(te)-62 b(orije)571
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49334 y(witc)-34 b(h)371 b(i)e(M.)g(T)-101 b(uruani)370
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b(grafo)-34 b(vima.)4317 55356 y(Stanje)346 b FG(S)414
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b(o)34 b(dre)p 38840 56248 364 53 v(den)509 b(p)34 b(o)2435
58367 y(za)-34 b(vr)-64 b(\267)-542 b(setku)382 b(inicijalizacijsk)-34
b(e)381 b(faze,)386 b FG(I)477 b FO(je)382 b(skup)350
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b(ama)338 b(na)h(mre)-34 b(\267)-572 b(zi,)351 b FG(A)339
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%%Page: 30 30
TeXDict begin HPSdict begin 30 29 bop 7749 7181 a FO(inicijalizacijsk)
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y FG(;)202 b(m)36902 46285 y FB(2)37427 46103 y FI(i)p
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b FG(cmp)h FO(rule,)16372 58403 y FN(I)p FO(\()p FG(m)18244
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FG(m)21854 58585 y FB(2)22380 58403 y FO(\))337 b FI(\241)-202
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71916 y(p)34 b(otrebno)270 b(te)f(ga)h(zanemarujemo.)24074
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%%Page: 31 31
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b(on)405 b(njih.)540 b FA(\244)4317 19258 y FO(Dok)-67
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b(jeg)404 b(donosi)h(normalizacija.)2435 25314 y FK(Dokaz.)704
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b(protok)-34 b(ola.)3311 35510 y(\(a\))607 b FG(S)6209
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b(na)p 9673 40167 364 53 v(di)410 b(pra)-34 b(vilo)408
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b FI(2)617 b FG(S)30839 40963 y FF(i)31623 40781 y FO(za)409
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b(j)p FG(X)95 b FI(j)-202 b(g)269 b(])g FG(I)365 b FI(])269
b FO(\246)3243 60489 y(\(b\))608 b(P)-34 b(ono)g(vi:)7122
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%%Page: 32 32
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%%Page: 33 33
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%%Page: 34 34
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b(izvo)-62 b(d)62 b(ljivosti)610 b FO(za)490 b(egzistencijalne)g(Horno)
-34 b(v)g(e)491 b(klauzule)f(je:)712 b(za)490 b(dani)i(skup)7749
67400 y FG(H)502 b FO(Horno)-34 b(vih)404 b(klauzula,)g(o)34
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b(dobit)338 b(\266)-572 b(cemo)371 b(da)h(uljez)f FI(I)461
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FG(X)500 b FO(izv)-34 b(o)34 b(dljiv)403 b(iz)g FG(H)98
b FO(.)27068 74956 y(34)p eop end end
%%Page: 35 35
TeXDict begin HPSdict begin 35 34 bop 2435 7181 a FO(Kak)-34
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y FH(3.6)1793 b(Egzistencijalne)599 b(Horno)-50 b(v)g(e)599
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b(zanemariti.)2435 22424 y FL(De\257nicija)465 b(12)606
b FK(Egzistencijalne)431 b(Hornove)h(klauzule)f(su)h(formule)g(oblika:)
3697 25193 y FI(8)p FG(x)5063 25375 y FB(1)5589 25193
y FI(8)p FG(x)6955 25375 y FB(2)7683 25193 y FG(:)202
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y FO([)p FG(\256)12153 25375 y FB(1)12949 25193 y FI(^)269
b FG(\256)14801 25375 y FB(2)15597 25193 y FI(^)g FG(:)202
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b FO(0)p FK(,)433 b FG(j)407 b FI(\270)336 b FO(0)p FK(,)434
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b(Hornovih)k(klauzula.)4317 36810 y FO(U)567 b(deduktivnom)h(sistem)-34
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b(B)p 27968 43832 5526 49 v 29113 44902 a(A)270 b FI(^)f
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61378 y(p)g(onensa\))453 b FG(P)168 b FO(\()8982 61154
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FG(=x)26445 61560 y FF(n)27071 61378 y FO(\),)464 b(tj.)452
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61378 y FO(supstituiran)2435 62884 y(nekim)314 b(termom)f
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b(vimo)314 b(isto,)2435 64389 y(zamjenimo)398 b FG(~)-589
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b FO(=)353 b(\()p FG(y)17968 64571 y FB(1)18495 64389
y FG(;)202 b(:)g(:)g(:)e(;)i(y)21782 64571 y FF(m)22670
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b(\267)-542 b(stene)2435 67400 y(me)p 4245 66786 364
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b(ti\257k)-67 b(atora.)21755 74956 y(35)p eop end end
%%Page: 36 36
TeXDict begin HPSdict begin 36 35 bop 9631 7181 a FO(Ovim)459
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b(\267)-572 b(cinjenice)368 b FG(F)537 b FO(za)7749 11698
y(k)-34 b(o)67 b(je)474 b(vrijedi)g(aksiom)g FG(tr)34
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b(vilo)474 b([)p FN(ax)p FO(].)749 b(Sta)-34 b(vimo)7749
13203 y(\242)8759 13385 y FB(1)9285 13203 y FO(:=)403
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b(su)g(deriv)-67 b(abilne)437 b(iz)g(\242)47223 14891
y FF(i)7749 16214 y FO(uz)422 b(dana)g(pra)-34 b(vila.)591
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b(d)422 b(dobiv)-67 b(amo)422 b(no)-34 b(v)g(e)388 b(\267)-572
b(cinjenice.)7749 17720 y(Kad)404 b(nijedno)h(pra)-34
b(vilo)404 b(vi)-64 b(\267)-542 b(se)403 b(ne)h(mo)-34
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b(je)f(skup)g(\242.)9631 19288 y(P)-34 b(ostupak)644
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b(k)-34 b(onjunk)g(cije)644 b(Horno)-34 b(v)g(e)7749
20794 y(teorije)416 b FG(H)98 b FO(:)563 b(sin)-34 b(takti)g(\267)-572
b(ck)-67 b(a)417 b(pra)-34 b(vila)416 b(direktno)g(re\260ektira)67
b(ju)417 b(seman)-34 b(tiku,)420 b(opisuju)-34 b(\266)-572
b(ci)354 b(\267)-542 b(sto)7749 22299 y(p)34 b(osta)67
b(je)397 b(istinito)g(u)f(no)-34 b(v)g(om)398 b(stanju)g(\242)25710
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b(olsk)g(e)356 b(teorije)7749 31283 y FO(Za)339 b(dan)-34
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b(teoriji)d FG(H)98 b FO(.)9631 38874 y(Sv)-67 b(ak)-34
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b(v)g(o)67 b(j)405 b(form)-34 b(uli)405 b FG(C)9011 41786
y FI(8)p FG(x)10377 41968 y FB(1)10903 41786 y FI(8)p
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b(:)g(:)f FI(9)p FG(y)35391 41968 y FF(j)36148 41786
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b(:)g(:)268 b FI(^)i FG(\257)45183 41983 y FF(l)45529
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b(k^)-606 b(od)545 b FI(d)p FG(C)87 b FI(e)p FO(,)580
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b(cin.)962 b(T)-101 b(o)546 b(je)f(skup)h(rola)f FG(R)9
b(ol)24 b(e)p FO(\()p FG(C)87 b FO(\),)581 b(k)-34 b(o)67
b(ji)545 b(se)7749 46204 y(sasto)67 b(ji)359 b(o)34 b(d)359
b(protok)-34 b(olsk)g(e)359 b(role)e FI(R)p FO(\()p FG(C)87
b FO(\),)369 b(k)-34 b(omp)34 b(ozicijsk)-34 b(e)358
b(role)f FI(C)71 b FO(\()p FG(C)87 b FO(\))360 b(i)e(dek)-34
b(omp)34 b(ozicijsk)-34 b(e)7749 47710 y(role)409 b FI(D)34
b FO(\()p FG(C)87 b FO(\).)556 b(Kasnije)409 b(je)h(ob)67
b(ja)-64 b(\267)-542 b(snjeno)412 b(k)-34 b(o)34 b(diranje)410
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49215 y FI(d)p FG(\256)9063 49397 y FB(1)9858 49215 y
FI(^)269 b FG(\256)11710 49397 y FB(2)12506 49215 y FI(^)g
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FO(\))405 b(za)f(gornju)h(klauzulu)f(je)8739 55202 y
FN(A)9547 55384 y FB(0)10073 55202 y FG(;)202 b FN(N)p
FO(\()p FI(d)p FG(\256)13256 55384 y FB(1)14051 55202
y FI(^)270 b FG(\256)15904 55384 y FB(2)16699 55202 y
FI(^)g FG(:)202 b(:)g(:)268 b FI(^)i FG(\256)21313 55399
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b FI(^)g FG(\257)45252 55399 y FF(l)45598 55202 y FI(e)p
FO(\))7749 58115 y(gdje)404 b(su)h FN(A)12705 58297 y
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b(k)-34 b(onzekv)g(en)g(te.)547 b(Uljez)406 b(je)h(ta)67
b(j)408 b(k)-34 b(o)67 b(ji)407 b(prenosi)g(p)34 b(oruk)-34
b(e,)408 b(i)7749 65705 y(moramo)332 b(m)-34 b(u)333
b(dati)g(mogu)-34 b(\266)-572 b(cnost)333 b(da)g(ih)f(transformira,)347
b(u)333 b(skladu)f(s)h(njego)-34 b(vim)332 b(sp)34 b(osob-)7749
67210 y(nostima.)578 b(Kada)417 b(dozna)g(k^)-606 b(od)417
b(k)-34 b(onjunk)g(cije,)422 b(trebao)417 b(bi)g(je)g(mo)-34
b(\266)-572 b(ci)416 b(analizirati,)j(i)e(k)-34 b(om-)7749
68716 y(p)34 b(onirati)635 b(s)h(v)-34 b(e)g(\266)-572
b(c)635 b(p)34 b(oznatim)603 b(\267)-572 b(cinjenicama.)1232
b(T)-101 b(ome)636 b(slu)-34 b(\267)-572 b(ze)635 b(dek)-34
b(omp)34 b(ozicijsk)-34 b(e)635 b(role,)7749 70221 y
FI(D)34 b FO(\()p FG(C)87 b FO(\):)16339 71916 y FN(B)17147
72098 y FF(i)17523 71916 y FG(;)202 b FN(N)p FO(\()p
FI(d)p FG(\257)20617 72098 y FB(1)21411 71916 y FI(^)270
b FG(\257)23175 72098 y FB(2)23970 71916 y FI(^)f FG(:)202
b(:)g(:)268 b FI(^)i FG(\257)28494 72113 y FF(k)29062
71916 y FI(e)p FO(\))337 b FI(\241)-202 b(!)337 b FN(B)33507
71416 y FE(0)33817 72098 y FF(i)34193 71916 y FG(;)202
b FN(N)p FO(\()p FI(d)p FG(\257)37287 72098 y FF(i)37662
71916 y FI(e)p FO(\))p FG(;)27068 74956 y FO(36)p eop
end end
%%Page: 37 37
TeXDict begin HPSdict begin 37 36 bop 2435 7181 a FO(p)34
b(o)404 b(jedna)h(za)f(sv)-67 b(aki)403 b FG(i)p FO(,)h(1)336
b FI(\267)h FG(i)f FI(\267)h FG(k)38 b FO(,)404 b(sa)g(svje)-34
b(\267)-572 b(zim)403 b FN(B)25441 7363 y FF(i)26221
7181 y FO(i)h FN(B)27770 6741 y FE(0)28080 7363 y FF(i)28860
7181 y FO(za)g(sv)-67 b(ak)-34 b(o)404 b(pra)-34 b(vilo.)4317
10219 y(Sli)g(\267)-572 b(cno,)525 b(za)500 b(sv)-67
b(aku)500 b(Horno)-34 b(vu)502 b(klauzulu)f FG(C)587
b FO(o)34 b(dgo)-34 b(v)-67 b(ara)67 b(ju)-34 b(\266)-572
b(ca)502 b(k)-34 b(omp)34 b(ozicijsk)-67 b(a)499 b(rola)2435
11724 y FI(C)71 b FO(\()p FG(C)87 b FO(\))405 b(mo)-34
b(\267)-572 b(ze)404 b(kreirati)f(k^)-606 b(od)404 b(k)-34
b(onjunk)g(cije)405 b(lijev)-34 b(e)403 b(strane.)539
b(Za)404 b(klauzulu)g FG(C)491 b FO(imamo:)17632 14490
y FN(C)18406 14672 y FB(0)18932 14490 y FG(;)202 b FN(N)p
FO(\()p FI(d)p FG(\256)22115 14672 y FB(1)22641 14490
y FI(e)p FO(\))1107 b FI(\241)-203 b(!)1108 b FN(C)28592
14672 y FB(1)29118 14490 y FO(\()p FI(d)p FG(\256)30903
14672 y FB(1)31429 14490 y FI(e)p FO(\))14310 15996 y
FN(C)15084 16178 y FB(1)15611 15996 y FO(\()p FI(d)p
FG(\256)17396 16178 y FB(1)17922 15996 y FI(e)p FO(\))p
FG(;)202 b FN(N)p FO(\()p FI(d)p FG(\256)22115 16178
y FB(2)22641 15996 y FI(e)p FO(\))1107 b FI(\241)-203
b(!)1108 b FN(C)28592 16178 y FB(2)29118 15996 y FO(\()p
FI(d)p FG(\256)30903 16178 y FB(1)31698 15996 y FI(^)270
b FG(\256)33551 16178 y FB(2)34077 15996 y FI(e)p FO(\))25027
17501 y FG(:)202 b(:)g(:)2989 19007 y FN(C)3763 19204
y FF(k)24 b FE(\241)p FB(2)5534 19007 y FO(\()p FI(d)p
FG(\256)7319 19189 y FB(1)8115 19007 y FI(^)269 b FG(\256)9967
19189 y FB(2)10763 19007 y FI(^)g FG(:)202 b(:)g(:)269
b FI(^)g FG(\256)15376 19204 y FF(k)24 b FE(\241)p FB(2)17148
19007 y FI(e)p FG(;)202 b FN(N)p FO(\()p FI(d)p FG(\256)20870
19204 y FF(k)24 b FE(\241)p FB(1)22641 19007 y FI(e)p
FO(\))1107 b FI(\241)-203 b(!)1108 b FN(C)28592 19204
y FF(k)24 b FE(\241)p FB(1)30363 19007 y FO(\()p FI(d)p
FG(\256)32148 19189 y FB(1)32944 19007 y FI(^)269 b FG(\256)34796
19189 y FB(2)35592 19007 y FI(^)g FG(:)202 b(:)g(:)269
b FI(^)g FG(\256)40205 19204 y FF(k)24 b FE(\241)p FB(1)41977
19007 y FI(e)p FO(\))3720 20512 y FN(C)4494 20709 y FF(k)g
FE(\241)p FB(1)6265 20512 y FO(\()p FI(d)p FG(\256)8050
20694 y FB(1)8846 20512 y FI(^)269 b FG(\256)10698 20694
y FB(2)11494 20512 y FI(^)g FG(:)202 b(:)g(:)269 b FI(^)g
FG(\256)16107 20709 y FF(k)24 b FE(\241)p FB(1)17879
20512 y FI(e)p FO(\))p FG(;)202 b FN(N)p FO(\()p FI(d)p
FG(\256)22072 20709 y FF(k)22641 20512 y FI(e)p FO(\))1107
b FI(\241)-203 b(!)1108 b FN(C)28592 20709 y FF(k)29161
20512 y FG(;)202 b FN(N)p FO(\()p FI(d)p FG(\256)32344
20694 y FB(1)33139 20512 y FI(^)269 b FG(\256)34991 20694
y FB(2)35787 20512 y FI(^)g FG(:)202 b(:)g(:)269 b FI(^)g
FG(\256)40400 20709 y FF(k)40969 20512 y FI(e)p FO(\))2435
23214 y(op)34 b(et)473 b(s)g(pretho)34 b(dno)474 b(nek)-34
b(ori)-64 b(\267)-542 b(stenim)473 b(predik)-67 b(atima)473
b FN(C)26843 23396 y FF(i)27219 23214 y FO(.)744 b(Uo)-34
b(\267)-572 b(cimo)473 b(da)g(je)g(samo)g(zadnji)2435
24720 y(k)-34 b(orak)513 b(k)-34 b(omp)34 b(ozicijsk)-34
b(e)512 b(role)g(druga)-34 b(\267)-572 b(ciji,)540 b(jer)513
b(sta)-34 b(vlja)513 b(k)-34 b(omp)34 b(oniran)-34 b(u)515
b(k)-34 b(onjunk)g(ciju)514 b(u)2435 26225 y(promet.)4317
29263 y(Kona)-34 b(\267)-572 b(cno,)404 b(k^)-606 b(od)405
b(k)-34 b(onjunk)g(cije)405 b(atomarnih)g(form)-34 b(ula)4390
32066 y FG(\256)5165 32248 y FB(1)5691 32066 y FO(\()p
FG(t)6600 32248 y FB(11)7596 32066 y FG(;)202 b(t)8573
32248 y FB(12)9569 32066 y FG(;)g(:)g(:)g(:)f(;)h(t)12701
32248 y FB(1)p FF(i)13491 32371 y Fk(1)14008 32066 y
FO(\))269 b FI(^)h FG(\256)16601 32248 y FB(2)17127 32066
y FO(\()p FG(t)18036 32248 y FB(21)19032 32066 y FG(;)202
b(t)20009 32248 y FB(22)21005 32066 y FG(;)g(:)g(:)g(:)f(;)h(t)24137
32248 y FB(2)p FF(i)24927 32371 y Fk(2)25444 32066 y
FO(\))270 b FI(^)f FG(:)202 b(:)g(:)269 b FI(^)g FG(\256)30798
32263 y FF(k)31367 32066 y FO(\()p FG(t)32276 32263 y
FF(k)24 b FB(1)33316 32066 y FG(;)202 b(t)34293 32263
y FF(k)24 b FB(2)35331 32066 y FG(;)202 b(:)g(:)g(:)f(;)h(t)38463
32263 y FF(k)24 b(i)39297 32419 y FC(k)39860 32066 y
FO(\))2402 34870 y(\266)-572 b(ce)403 b(biti)9166 36456
y FN(enc)p FO(\()p FG(K)19 b(;)202 b FI(h)p FG(\256)14174
36638 y FB(1)14701 36456 y FG(\256)15476 36638 y FB(2)16205
36456 y FG(:)g(:)g(:)f(\256)18596 36653 y FF(k)19165
36456 y FG(;)h(t)20142 36638 y FB(11)21138 36456 y FG(;)g(:)g(:)g(:)f
(;)h(t)24270 36638 y FB(1)p FF(i)25060 36761 y Fk(1)25576
36456 y FG(;)g(:)g(:)g(:)f(;)h(t)28708 36653 y FF(k)24
b FB(1)29747 36456 y FG(;)202 b(:)g(:)g(:)f(;)h(t)32879
36653 y FF(k)24 b(i)33713 36809 y FC(k)34276 36456 y
FI(i)p FO(\))p FG(;)4239 b FO(\(3.3\))2435 38775 y(gdje)270
b(je)g FG(\256)6847 38957 y FB(1)7373 38775 y FG(\256)8148
38957 y FB(2)8876 38775 y FG(:)202 b(:)g(:)f(\256)11267
38972 y FF(k)12106 38775 y FO(no)-34 b(vi)269 b(k)-34
b(onstan)g(tski)272 b(sim)-34 b(b)34 b(ol,)296 b(razli)-34
b(\267)-572 b(cit)268 b(za)h(sv)-67 b(aki)268 b(niz)h
FG(\256)35766 38957 y FB(1)36293 38775 y FG(;)202 b(\256)37607
38957 y FB(2)38133 38775 y FG(;)g(:)g(:)g(:)e(;)i(\256)41601
38972 y FF(k)42170 38775 y FO(,)2435 40280 y(a)404 b
FG(K)492 b FO(proizv)-34 b(oljni)404 b(enkrip)34 b(cijski)402
b(klju)-34 b(\267)-572 b(c)371 b(\267)-572 b(ciji)403
b(dekrip)34 b(cijski)403 b(in)-34 b(v)g(erz)403 b(nije)i(p)34
b(oznat)404 b(uljezu.)4317 43318 y(Za)447 b(Horno)-34
b(vu)449 b(teoriju)e FG(H)98 b FO(,)458 b(k)-34 b(o)67
b(ja)449 b(je)e(skup)h(Horno)-34 b(vih)448 b(klauzula)f
FG(C)87 b FO(,)458 b(ozna)-34 b(\267)-572 b(cimo)448
b(sa)2435 44824 y FI(T)309 b FO(\()p FG(H)98 b FO(\))404
b(opisan)-34 b(u)406 b(protok)-34 b(olsku)405 b(teoriju,)f(skup)h(rola)
e(za)h(sv)-67 b(aku)404 b FG(C)87 b FO(.)2435 49324 y
FL(Lema)464 b(2)606 b FK(Neka)437 b(je)f FI(T)308 b FO(\()p
FG(H)98 b FO(\))439 b FK(opisano)c(ko)-62 b(dir)g(anje)435
b(Hornove)h(te)-62 b(orije)436 b FG(H)535 b FK(u)437
b(pr)-62 b(otokolsku)2435 50829 y(te)g(oriju.)682 b(T)-93
b(ada)475 b(je)h FG(X)95 b FK(-)-31 b(\267)-589 b(cinjenic)-62
b(a)474 b(izvo)-62 b(d)62 b(ljiva)472 b(u)k FG(H)574
b FK(akko)474 b(pr)-62 b(otokolska)472 b(te)-62 b(orija)474
b FI(T)308 b FO(\()p FG(H)98 b FO(\))2435 52335 y FK(zaje)-62
b(dno)432 b(sa)h(uljezovom)d(te)-62 b(orijom)432 b FI(I)523
b FK(vo)-62 b(di)433 b(u)g(stanje)f(koji)g(sadr)-62 b(\267)-558
b(zi)432 b FN(I)p FO(\()p FI(d)p FG(X)95 b FI(e)p FO(\))p
FK(.)2435 55303 y(Dokaz.)616 b FO(Dok)-67 b(az)429 b(u)i(oba)f(smjera)h
(ide)f(induk)-34 b(cijom.)618 b(P)-34 b(ok)-67 b(a)-34
b(\267)-572 b(zimo)429 b(prv)-34 b(o)431 b(da)f(ak)-34
b(o)431 b(p)34 b(osto)67 b(ji)2435 56808 y(stanje)405
b(sa)371 b(\267)-572 b(cinjenicom)404 b FN(I)p FO(\()p
FI(d)p FG(X)95 b FI(e)p FO(\),)404 b(tada)g(je)h FG(X)499
b FO(izv)-34 b(o)34 b(dljiv)-67 b(a)403 b(iz)g FG(H)98
b FO(.)4317 58340 y FK(Baza)562 b(indukcije.)959 b FO(Ak)-34
b(o)546 b FN(I)p FO(\()p FI(d)p FG(X)95 b FI(e)p FO(\))545
b(u)g(prv)-34 b(om)546 b(k)-34 b(oraku,)580 b(o)34 b(dnosno)546
b(prv)-34 b(om)545 b(stanju,)2435 59846 y(uljez)437 b(ga)f(je)h(saznao)
f(s)h(mre)-34 b(\267)-572 b(ze.)634 b(Odgo)-34 b(v)-67
b(ara)67 b(ju)-34 b(\266)-572 b(ce)437 b(pra)-34 b(vilo)436
b(k)-34 b(o)67 b(je)437 b(to)g(opisuje)g(je)g FN(A)39417
60028 y FB(0)40333 59846 y FI(\241)-202 b(!)2435 61351
y FN(A)3243 61533 y FB(1)3769 61351 y FG(;)202 b FN(N)p
FO(\()p FI(d)p FG(X)95 b FI(e)p FO(\),)340 b(\267)-542
b(sto)404 b(o)34 b(dgo)-34 b(v)-67 b(ara)404 b(klauzuli)g
FG(tr)34 b(ue)336 b FO(=)-202 b FI(\))337 b FG(X)95 b
FO(.)4317 62884 y FK(Kor)-62 b(ak)438 b(indukcije.)552
b FO(Ak)-34 b(o)409 b FN(I)p FO(\()p FI(d)p FG(X)95 b
FI(e)p FO(\))410 b(pripada)g(stanju)h(nek)-34 b(og)410
b FG(n)p FO(tog)g(k)-34 b(orak)-67 b(a,)409 b(tada)i(je)2435
64389 y(uljez)489 b(mogao)g(doznati)g FI(d)p FG(X)95
b FI(e)488 b FO(iz)g FN(N)p FO(\()p FI(d)p FG(X)95 b
FI(e)p FO(\),)510 b(pra)-34 b(vilom)488 b FG(r)34 b(ec)p
FO(.)792 b(Nije)488 b(se)h(moglo)f(raditi)h(o)2435 65894
y(dekrip)34 b(ciji,)373 b(na)368 b(primjer,)374 b(zb)34
b(og)367 b(na)-34 b(\267)-572 b(cina)367 b(na)g(k)-34
b(o)67 b(ji)368 b(je)f FI(T)308 b FO(\()p FG(H)98 b FO(\))368
b(de\257nirana,)375 b(i)367 b(k)-34 b(onjunk)g(cije)2435
67400 y(k)g(o)34 b(dirane)271 b({)f(uljez)h(ne)f(p)34
b(osjeduje)272 b(priv)-67 b(atni)270 b(in)-34 b(v)g(erz)270
b(klju)-34 b(\267)-572 b(ca)271 b(k)-34 b(o)67 b(jom)271
b(su)g(p)34 b(oruk)-34 b(e)207 b(\267)-542 b(sifrirane.)2435
68905 y(T)-101 b(ak)-34 b(o)p 5289 68292 364 53 v(der,)482
b(pra)-34 b(vilo)466 b(iz)f(k)-34 b(o)67 b(jeg)467 b(je)f(uljez)g
(saznao)h FI(d)p FG(X)95 b FI(e)466 b FO(nije)g(enkrip)34
b(cija)465 b({)h(tada)h(bi)f(v)-34 b(e)g(\266)-572 b(c)2435
70411 y(prije)348 b(morao)h(imati)f FG(X)95 b FO(,)359
b(a)348 b(to)h(je)f(op)34 b(et)349 b(mogao)f(doznati)h(samo)g(iz)f
FI(d)p FG(X)95 b FI(e)p FO(.)519 b(Nije)348 b(se)g(radilo)2435
71916 y(niti)405 b(o)f(pra)-34 b(vilima)403 b FG(cmp)p
FO(,)h FG(dcmp)f FO(ili)g FG(nnc)p FO(.)21755 74956 y(37)p
eop end end
%%Page: 38 38
TeXDict begin HPSdict begin 38 37 bop 9766 6875 a FO(\267)9631
7181 y(Cinjenica)324 b FN(N)p FO(\()p FI(d)p FG(X)95
b FI(e)p FO(\))324 b(je)h(p)34 b(osljedica)324 b(nek)-34
b(og)324 b(pra)-34 b(vila)324 b(role,)339 b(dek)-34 b(omp)34
b(ozicije)324 b(ili)f(k)-34 b(om-)7749 8687 y(p)34 b(ozicije.)7749
10192 y(Ak)-34 b(o)404 b(je)g(pra)-34 b(vilo)404 b(bilo)g(tipa)g
FI(R)p FO(\()p FG(C)87 b FO(\),)16472 12947 y FN(A)17280
13129 y FB(0)17806 12947 y FG(;)202 b FN(N)p FO(\()p
FI(d)p FG(X)21313 12446 y FE(0)21623 12947 y FI(e)p FO(\))337
b FI(\241)-202 b(!)337 b(9)p FG(y)26527 13129 y FB(1)27053
12947 y FI(9)p FG(y)28320 13129 y FB(2)29049 12947 y
FG(:)202 b(:)g(:)f FI(9)p FG(y)31932 13129 y FF(j)32689
12947 y FN(A)33497 13129 y FB(1)34023 12947 y FG(;)h
FN(N)p FO(\()p FI(d)p FG(X)95 b FI(e)p FO(\))p FG(;)7749
15702 y FO(tada)443 b(je)g(u)f(pretho)34 b(dnom)444 b(stanju)g(p)34
b(osto)67 b(jala)410 b(\267)-572 b(cinjenica)442 b FN(N)p
FO(\()p FI(d)p FG(X)36928 15262 y FE(0)37239 15702 y
FI(e)p FO(\))g(u)h(an)-34 b(teceden)g(ti,)453 b(te)7749
17207 y(je)320 b(uljez)h(imao)f FI(d)p FG(X)16274 16767
y FE(0)16585 17207 y FI(e)g FO(u)h(sv)-34 b(o)67 b(jo)g(j)322
b(memoriji.)510 b(P)-34 b(o)320 b(hip)34 b(otezi)321
b(induk)-34 b(cije,)337 b(p)34 b(osto)67 b(ji)322 b FG(H)98
b FO({izv)-34 b(o)34 b(d)7749 18713 y(za)404 b FG(X)10397
18273 y FE(0)10707 18713 y FO(,)g(i)g(iz)f(zadnjeg)i(pra)-34
b(vila)404 b FI(R)p FO(\()p FG(C)87 b FO(\))405 b(direktno)f(o)-34
b(\267)-572 b(citamo)404 b(klauzulu)h FG(C)17450 21467
y FI(8)p FG(x)18816 21649 y FB(1)19342 21467 y FI(8)p
FG(x)20708 21649 y FB(2)21436 21467 y FG(:)202 b(:)g(:)f
FI(8)p FG(x)24418 21649 y FF(i)25064 21467 y FG(X)26163
20967 y FE(0)26810 21467 y FO(=)-202 b FI(\))337 b(9)p
FG(y)30367 21649 y FB(1)30893 21467 y FI(9)p FG(y)32160
21649 y FB(2)32889 21467 y FG(:)202 b(:)g(:)f FI(9)p
FG(y)35772 21649 y FF(j)36529 21467 y FG(X)28 b(:)7749
24222 y FO(F)-101 b(orm)-34 b(ula)366 b(\267)-572 b(cini)399
b FG(X)495 b FO(izv)-34 b(o)34 b(dljiv)-34 b(om)400 b(iz)f
FG(X)25131 23782 y FE(0)25442 24222 y FO(,)h(k)-34 b(oriste)g(\266)-572
b(ci)399 b([)p FI(89)p FO(])h(pra)-34 b(vilo)399 b(sistema,)367
b(\267)-572 b(cime)399 b(dobi-)7749 25728 y(jemo)404
b FG(H)98 b FO({izv)-34 b(o)34 b(d)404 b(o)34 b(d)404
b FG(X)95 b FO(.)7749 27233 y(Ak)-34 b(o)514 b(je)g(bilo)g(k)-34
b(ori)-64 b(\267)-542 b(steno)514 b(pra)-34 b(vilo)513
b(dek)-34 b(omp)34 b(ozicije,)541 b(uljez)514 b(je)g(morao)g(nau)-34
b(\267)-572 b(citi)514 b FI(d)p FG(X)45923 27415 y FB(1)46791
27233 y FI(^)7749 28739 y FG(:)202 b(:)g(:)332 b FI(^)g
FG(X)11640 28921 y FF(n)12267 28739 y FI(e)499 b FO(u)g(nek)-34
b(om)500 b(ranijem)f(stanju,)524 b(gdje)500 b(je)f FG(X)595
b FO(jedan)500 b(o)34 b(d)499 b(k)-34 b(onjunk)-67 b(ata.)825
b(T)-101 b(ada)7749 30244 y FG(H)608 b FI(`)510 b FG(X)11620
30426 y FB(1)12485 30244 y FI(^)338 b FG(:)202 b(:)g(:)338
b FI(^)h FG(X)17535 30426 y FF(n)18161 30244 y FO(,)534
b(te)509 b(za)67 b(jedno)509 b(s)f(pra)-34 b(vilima)508
b(izv)-34 b(o)34 b(da)507 b([)p FI(^)p FG(LE)70 b FO(])507
b(i)h([)p FI(^)p FG(R)9 b(E)70 b FO(])508 b(imamo)7749
31749 y(izv)-34 b(o)34 b(d)403 b(o)34 b(d)405 b FG(X)95
b FO(.)7749 33255 y(Ak)-34 b(o)372 b(su)g(k)-34 b(ori)-64
b(\267)-542 b(stena)373 b(pra)-34 b(vila)371 b(k)-34
b(omp)34 b(ozicije,)378 b FG(X)467 b FO(je)372 b(morala)g(biti)g(oblik)
-67 b(a)371 b FG(X)41312 33437 y FB(1)42044 33255 y FI(^)205
b FG(:)d(:)g(:)i FI(^)i FG(X)46694 33452 y FF(k)47263
33255 y FO(.)7749 34760 y(Kroz)431 b(k)-34 b(omp)34 b(ozicijsk)-67
b(a)430 b(pra)-34 b(vila,)438 b(uljez)432 b(je)g(redom)f(nau)-34
b(\267)-572 b(cio)432 b FN(I)p FO(\()p FI(d)p FG(X)37084
34942 y FB(1)37610 34760 y FI(e)p FO(\))p FG(;)202 b(:)g(:)g(:)f(;)h
FN(I)p FO(\()p FI(d)p FG(X)43665 34957 y FF(k)44234 34760
y FI(e)p FO(\).)621 b(P)-34 b(o)7749 36266 y(pretp)34
b(osta)-34 b(v)g(ci)434 b(induk)-34 b(cije,)442 b FG(H)484
b FI(`)386 b FG(X)23806 36448 y FF(i)24616 36266 y FO(za)434
b(sv)-67 b(aki)432 b FG(i)386 b FO(=)g(1)p FG(;)202 b(:)g(:)g(:)f(;)h
(k)38 b FO(,)441 b(pa)435 b(zaklju)-34 b(\267)-572 b(cujemo)434
b FG(X)529 b FO(iz)7749 37771 y FG(X)8753 37953 y FB(1)9279
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b FO(pra)-34 b(vila)404 b(izv)-34 b(o)34 b(da)404 b([)p
FI(^)p FG(I)95 b FO(].)9631 40793 y(Sada)405 b(pretp)34
b(osta)-34 b(vimo)404 b(da)h(p)34 b(osto)67 b(ji)405
b(izv)-34 b(o)34 b(d)404 b(za)g FG(X)499 b FO(iz)403
b FG(H)98 b FO(,)404 b FG(H)435 b FI(`)336 b FG(X)95
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FO(onda)534 b(vrijedi)7749 43814 y FG(tr)34 b(ue)336
b FO(=)-202 b FI(\))337 b FG(X)95 b FO(.)538 b(Odgo)-34
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b(vilo)403 b(role)h(za)g(tu)g(klauzulu)h(je)22600 46569
y FN(A)23408 46751 y FB(0)24271 46569 y FI(\241)-202
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b FN(N)p FO(\()p FI(d)p FG(X)95 b FI(e)p FO(\))p FG(:)7749
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b(p)34 b(otreban)387 b FN(A)25063 51011 y FB(0)25589
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b(o)629 b(je)596 b(\267)-572 b(cinjenica)629 b FG(X)724
b FO(p)34 b(osljedica)630 b(nek)-34 b(og)629 b FG(n)p
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b(nek)-34 b(o)332 b(o)34 b(d)333 b(pra)-34 b(vila)7749
56862 y([)p FI(^)p FG(LE)70 b FO(],)510 b([)p FI(^)p
FG(R)9 b(E)70 b FO(],)510 b([)p FI(89)p FO(].)796 b(Pra)-34
b(vilo)489 b([)p FI(^)p FG(I)95 b FO(])489 b(ne)h(izv)-34
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b(stena)322 b(je)g(form)-34 b(ula)322 b FI(8)p FG(x)30583
60055 y FB(1)31109 59873 y FI(8)p FG(x)32475 60055 y
FB(2)33203 59873 y FG(:)202 b(:)g(:)f FI(8)p FG(x)36185
60055 y FF(i)36561 59873 y FO([)p FG(\256)37673 60055
y FB(1)38303 59873 y FI(^)105 b FG(\256)39991 60055 y
FB(2)40622 59873 y FI(^)g FG(:)202 b(:)g(:)103 b FI(^)i
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FI(\))7749 61378 y(9)p FG(y)9016 61560 y FB(1)9542 61378
y FI(9)p FG(y)10809 61560 y FB(2)11538 61378 y FG(:)202
b(:)g(:)f FI(9)p FG(y)14421 61560 y FF(j)15287 61378
y FG(X)95 b FO(],)609 b(neprazne)569 b(an)-34 b(teceden)g(te.)1032
b(Pretho)34 b(dno)569 b(je)g(u)g(\242)40392 61560 y FF(n)p
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62884 y(junk)g(cija)587 b(\267)-572 b(cinjenica)619 b
FG(\256)18551 63066 y FB(1)19491 62884 y FI(^)413 b FG(\256)21487
63066 y FB(2)22427 62884 y FI(^)g FG(:)202 b(:)g(:)413
b FI(^)g FG(\256)27472 63081 y FF(k)28041 62884 y FO(.)1186
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b(olsk)g(o)67 b(j)7749 64389 y(teoriji)545 b(o)34 b(dgo)-34
b(v)-67 b(ara)67 b(ju)-34 b(\266)-572 b(ce)545 b(role)g
FI(R)p FO(\()p 22986 64389 364 45 v 437 w(\),)581 b FI(D)34
b FO(\()p 26252 64389 V 436 w(\),)581 b FI(C)71 b FO(\()p
29257 64389 V 436 w(\).)963 b(P)-34 b(o)546 b(pretp)34
b(osta)-34 b(v)g(ci)546 b(induk)-34 b(cije)545 b(bilo)7749
65894 y(je)404 b FN(I)p FO(\()p FI(d)p FG(\256)11184
66076 y FB(1)11979 65894 y FI(^)270 b FG(\256)13832 66076
y FB(2)14627 65894 y FI(^)g FG(:)202 b(:)g(:)268 b FI(^)i
FG(\256)19241 66091 y FF(k)19810 65894 y FI(e)p FO(\).)538
b(Koriste)-34 b(\266)-572 b(ci)403 b FI(R)p FO(\()p 28394
65894 V 437 w(\))i(direktno)f(dobijemo)h FI(d)p FG(X)95
b FI(e)p FO(.)7749 67400 y(Ak)-34 b(o)491 b(je)h(zadnje)g(pra)-34
b(vilo)491 b(iz)g(k)-34 b(o)67 b(jeg)492 b(je)g(zaklju)-34
b(\267)-572 b(ceno)491 b FG(X)587 b FO(iz)491 b(dane)h(Horno)-34
b(v)g(e)492 b(teorije)f FG(H)7749 68905 y FO(bilo)522
b([)p FI(^)p FG(LE)70 b FO(])522 b(ili)g([)p FI(^)p FG(R)9
b(E)70 b FO(],)552 b(za)523 b(to)g(smo)g(k)-34 b(oristili)522
b(k)-34 b(onjunk)g(ciju)491 b(\267)-572 b(cinjenica)522
b FG(X)42997 69087 y FB(1)43872 68905 y FI(^)349 b FG(:)202
b(:)g(:)347 b FI(^)7749 70411 y FG(X)8753 70593 y FF(n)9379
70411 y FO(.)833 b(Nara)-34 b(vno,)526 b FG(X)598 b FO(je)502
b(jedan)h(o)34 b(d)502 b(k)-34 b(onjunk)-67 b(ata.)834
b(Ona)502 b(je)g(morala)g(biti)g(dobiv)-34 b(ena)503
b(u)7749 71916 y(nek)-34 b(om)351 b(k)-34 b(oraku)351
b(prije,)361 b(iz)350 b(Horno)-34 b(v)g(e)351 b(form)-34
b(ule)351 b FI(8)p FG(x)30233 72098 y FB(1)30759 71916
y FI(8)p FG(x)32125 72098 y FB(2)32853 71916 y FG(:)202
b(:)g(:)f FI(8)p FG(x)35835 72098 y FF(i)36211 71916
y FO([)p FG(\256)37323 72098 y FB(1)38012 71916 y FI(^)163
b FG(\256)39758 72098 y FB(2)40447 71916 y FI(^)g FG(:)202
b(:)g(:)162 b FI(^)h FG(\256)44741 72113 y FF(k)45646
71916 y FO(=)-202 b FI(\))27068 74956 y FO(38)p eop end
end
%%Page: 39 39
TeXDict begin HPSdict begin 39 38 bop 2435 7181 a FI(9)p
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y FB(2)6224 7181 y FG(:)202 b(:)g(:)f FI(9)p FG(y)9107
7363 y FF(j)9886 7181 y FG(X)10890 7363 y FB(1)11708
7181 y FI(^)291 b FG(:)202 b(:)g(:)291 b FI(^)g FG(X)16616
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b(olsk)g(e)405 b(role.)10055 8380 y(\267)9920 8687 y(Cinjenicu)g
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11326 y FI(^)270 b FG(:)202 b(:)g(:)268 b FI(^)i FG(X)22172
11508 y FF(n)22798 11326 y FI(e)p FO(\))337 b FI(\241)-202
b(!)337 b FN(D)27310 10825 y FE(0)27621 11326 y FG(;)202
b FN(N)p FO(\()p FI(d)p FG(X)95 b FI(e)p FO(\))p FG(:)2435
13964 y FO(P)-34 b(o)447 b(pretp)34 b(osta)-34 b(v)g(ci)448
b(induk)-34 b(cije,)458 b(p)34 b(osto)67 b(ji)448 b FN(I)p
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FI(^)298 b FG(:)202 b(:)g(:)297 b FI(^)h FG(X)28935 14146
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b(o)p 6669 14856 364 53 v(der)404 b(mo)-34 b(\267)-572
b(ze)404 b(do)-34 b(\266)-572 b(ci)404 b(i)g(do)g FI(d)p
FG(X)95 b FI(e)p FO(.)538 b FA(\244)2435 18219 y FL(Lema)464
b(3)606 b FK(Opisana)433 b(konstrukcija)d(p)-62 b(osti)g(\267)-558
b(ze)431 b(se)i(u)g(p)-62 b(olinomnom)433 b(vr)-62 b(emenu.)2435
20969 y(Dokaz.)501 b FO(Za)295 b(dan)-34 b(u)297 b(teoriju)f
FG(H)393 b FO(o)34 b(d)295 b FG(n)g FO(klauzula,)317
b(treba)296 b(formirati)f FG(n)g FO(rola)g({)g(jedan)h(k)-34
b(orak)2435 22474 y(je)317 b(p)34 b(otreban)318 b(za)f(protok)-34
b(olsku)317 b(rolu,)334 b(manje)318 b(o)34 b(d)317 b
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b(ozicijsku)317 b(rolu)2435 23980 y(i)417 b(manje)h(o)34
b(d)417 b FG(m)g FO(k)-34 b(orak)-67 b(a)417 b(za)g(k)-34
b(omp)34 b(ozicijsku)417 b(rolu,)j(gdje)d(je)g FG(m)h
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b(k)-34 b(onjunk)g(cije.)2435 30002 y(Sv)g(e)361 b(za)67
b(jedno,)370 b(o)-34 b(v)-67 b(ak)g(a)-34 b(v)361 b(prijev)-34
b(o)34 b(d)360 b(Horno)-34 b(v)g(e)362 b(teorije)e FG(H)459
b FO(u)361 b(protok)-34 b(olsku)362 b(teoriju)f FI(T)308
b FO(\()p FG(H)98 b FO(\))2435 31507 y(p)34 b(osti)-34
b(\267)-572 b(ze)404 b(se)g(u)g FI(O)34 b FO(\()p FG(mn)p
FO(\))405 b(k)-34 b(orak)-67 b(a.)538 b FA(\244)2435
35313 y FH(3.7)1793 b(Egzistencijalne)400 b(Horno)-50
b(v)g(e)400 b(klauzule)f(su)h(neo)50 b(dlu)-50 b(\267)-847
b(civ)-50 b(e)2435 38019 y FO(T)-101 b(ablo)405 b(deterministi)-34
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b(stro)67 b(ja)405 b(mo)-34 b(\267)-572 b(ze)404 b(se)h(opisati)f(skup)
34 b(om)405 b(egzisten-)2435 39524 y(cijalnih)437 b(Horno)-34
b(vih)436 b(form)-34 b(ula.)636 b(T)-101 b(o)437 b(p)34
b(o)-34 b(vla)g(\267)-572 b(ci)435 b(neo)34 b(dlu)-34
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b(teorija.)634 b(Radi)2435 41030 y(se)487 b(o)g(tablou)h(Co)34
b(ok)-34 b(o)g(v)g(og)488 b(stila.)786 b(Pretp)34 b(osta)-34
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b(cn)-34 b(u)489 b(traku)2435 42535 y(neome)p 6063 41921
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b(at)371 b(\266)-572 b(cemo)404 b(p)34 b(o)404 b(jedno)h(p)34
b(olje)404 b(udesno.)4317 48557 y(T)-101 b(uringo)-34
b(v)612 b(stro)67 b(j)612 b FG(M)742 b FO(zadan)612 b(je)f(sa)g
FI(h)p FO(\247)p FG(;)202 b(Q;)g(Q)25940 48745 y FF(F)26722
48557 y FG(;)g(q)27802 48739 y FB(0)28328 48557 y FG(;)g(\261)46
b FI(i)p FO(,)661 b(gdje)612 b(je)f(\247)g(proizv)-34
b(oljni)2435 50062 y(\(k)g(ona)g(\267)-572 b(cni\))509
b(alfab)34 b(et,)533 b(sa)508 b(sp)34 b(ecijalnim)507
b(sim)-34 b(b)34 b(olom)508 b FA(\244)p FO(,)533 b FG(Q)508
b FO(\(k)-34 b(ona)g(\267)-572 b(cni\))509 b(neprazni)e(skup)2435
51568 y(stanja,)554 b FG(Q)7488 51756 y FF(F)8804 51568
y FI(\265)535 b FG(Q)523 b FO(neprazni)g(skup)g(za)-34
b(vr)-64 b(\267)-542 b(snih)523 b(stanja.)896 b(Stanje)524
b FG(q)33532 51750 y FB(0)34581 51568 y FO(pripada)g(skupu)2435
53073 y FG(Q)428 b FO(i)g(to)g(je)g(p)34 b(o)-34 b(\267)-572
b(cetno)428 b(stanje,)434 b FG(\261)474 b FO(je)428 b(skup)g
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b(ti)2435 54579 y(funk)g(cije:)535 b(\()p FG(Q)254 b
FI(\243)e FO(\247\))338 b FI(\241)-203 b(!)337 b FG(Q)253
b FI(\243)g FO(\247)g FI(\243)f FG(M)132 b(ov)43 b(e)p
FO(,)397 b(gdje)g(je)e FG(M)132 b(ov)43 b(e)337 b FO(=)g
FI(f)p FG(L;)202 b(R)9 b FI(g)396 b FO(skup)g(p)34 b(omak)-67
b(a)2435 56084 y(gla)-34 b(v)g(e)390 b(stro)67 b(ja,)393
b(nalijev)-34 b(o)390 b(i)f(nadesno.)535 b(U)390 b(jednom)g(k)-34
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63032 y FI(\262)607 b FN(Adj)p FO(\()p FG(x;)202 b(y)43
b FO(\))405 b(:)539 b(p)34 b(olja)404 b FG(x)g FO(i)g
FG(y)447 b FO(su)405 b(susjedna;)4253 65506 y FI(\262)607
b FN(Bel)o FO(\()p FG(x;)202 b(y)43 b FO(\))405 b(:)538
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b(p)34 b(olja)405 b FG(x)p FO(;)4253 67979 y FI(\262)607
b FN(Cont)p FO(\()p FG(x;)202 b(a;)g(q)43 b FO(\))404
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67 b(j)405 b(u)f(stanju)i FG(q)43 b FO(.)4317 70411 y(Ak)-34
b(o)537 b(je)h FN(Cont)p FO(\()p FG(x;)202 b(a;)g(q)43
b FO(\))538 b(istinito,)570 b(to)538 b(zna)-34 b(\267)-572
b(ci)536 b(da)i(gla)-34 b(v)-67 b(a)537 b(stro)67 b(ja,)571
b(k)-34 b(o)67 b(ji)537 b(je)h(u)f(stanju)2435 71916
y FG(q)43 b FO(,)480 b(upra)-34 b(v)g(o)432 b(\267)-572
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b(olja)465 b FG(x)p FO(.)719 b(Ak)-34 b(o)431 b(\267)-572
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b(\267)-572 b(za)67 b(j)465 b(p)34 b(olja)465 b FG(x)21755
74956 y FO(39)p eop end end
%%Page: 40 40
TeXDict begin HPSdict begin 40 39 bop 7749 7181 a FO(upra)-34
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FO(\()p FG(x;)202 b(a;)p 13148 8687 364 45 v 638 w FO(\),)404
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b FO(\247)7749 13222 y(ozna)-34 b(\267)-572 b(ca)-34
b(v)-67 b(a)404 b(sadr)-34 b(\267)-572 b(za)67 b(j)404
b(rubnih)372 b(\266)-572 b(celija.)9631 16252 y(Slijedi)269
b(prijev)-34 b(o)34 b(d)270 b(T)-101 b(uringo)-34 b(v)g(og)271
b(stro)67 b(ja)270 b FG(M)402 b FO(s)270 b(ulaznom)g(rije)-34
b(\267)-572 b(ci)268 b FG(w)302 b FO(u)270 b(Horno)-34
b(vu)271 b(teoriju)7749 17757 y FG(H)98 b FO(\()p FG(M)65
b(;)202 b(w)33 b FO(\).)9631 20787 y FL(Inicijalizacija:)486
b FO(ulaz)304 b(na)g(traci)f(T)-101 b(uringo)-34 b(v)g(og)305
b(stro)67 b(ja)304 b(je)g(rije)-34 b(\267)-572 b(c)303
b FG(w)369 b FO(=)336 b FG(w)42031 20969 y FB(1)42557
20787 y FG(w)43425 20969 y FB(2)44152 20787 y FG(:)202
b(:)g(:)g(w)46637 20969 y FF(n)47263 20787 y FO(,)7749
22292 y(pritom)314 b(je)h FG(w)13727 22474 y FF(i)14416
22292 y FO(sadr)-34 b(\267)-572 b(za)67 b(j)315 b FG(i)p
FO(-te)280 b(\266)-572 b(celije)313 b(u)i(n)-34 b(ultom)315
b(k)-34 b(oraku)314 b(ra)-34 b(\267)-572 b(cuna)315 b(stro)67
b(ja.)510 b(Gla)-34 b(v)-67 b(a)313 b(je)i(p)34 b(ozi-)7749
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b(olju,)494 b(lijev)-34 b(o)474 b(o)34 b(d)476 b(tog)g(p)34
b(olja)475 b(je)g(oznak)-67 b(a)475 b FA(F)p FO(,)493
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b(a)398 b(prazna)g(p)34 b(olja)399 b(prije)e(desnog)i(kra)67
b(ja)399 b(je)f(slu)-34 b(\267)-572 b(ca)67 b(j)398 b
FG(w)369 b FO(=)337 b FG(\262)p FO(,)399 b(p)34 b(o)-34
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b(c)382 b(je)h(prazna,)388 b(gdje)383 b(su)h(nam)g(p)34
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32850 y(Situaciju)h(na)f(traci)g(opisujemo)h(skup)34
b(om)371 b(\267)-572 b(cinjenica:)8576 35629 y FI(f)p
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35811 y Fz(n)26459 35629 y FG(;)g FN(c)27537 35811 y
Fz(n)p FB(+)p Fz(1)29280 35629 y FO(\))p FG(;)g FN(Adj)p
FO(\()p FN(c)33057 35811 y Fz(n)p FB(+)p Fz(1)34801 35629
y FG(;)g FN(c)35879 35811 y Fz(n)p FB(+)p Fz(2)37622
35629 y FO(\))p FG(;)g FN(Adj)p FO(\()p FN(c)41399 35811
y Fz(n)p FB(+)p Fz(2)43143 35629 y FG(;)g FN(c)44221
35811 y Fz(n)p FB(+)p Fz(3)45964 35629 y FO(\))p FG(;)10754
38465 y FN(Cont)p FO(\()p FN(c)14208 38647 y Fz(0)14734
38465 y FG(;)g FA(F)p FG(;)p 17029 38465 V 638 w FO(\))p
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38465 y FG(;)g(w)23790 38647 y FB(1)24316 38465 y FG(;)g(q)25396
38647 y FB(0)25921 38465 y FO(\))p FG(;)g FN(Cont)p FO(\()p
FN(c)30385 38647 y Fz(2)30912 38465 y FG(;)g(w)32319
38647 y FB(2)32844 38465 y FG(;)p 33456 38465 V 638 w
FO(\))p FG(;)g(:)g(:)g(:)g(;)g FN(Cont)p FO(\()p FN(c)40439
38647 y Fz(n)40980 38465 y FG(;w)42185 38647 y FF(n)42811
38465 y FG(;)p 43422 38465 V 638 w FO(\))p FG(;)14812
40813 y FN(Cont)p FO(\()p FN(c)18266 40995 y Fz(n)p FB(+)p
Fz(1)20010 40813 y FG(;)g FA(\244)p FG(;)p 22103 40813
V 637 w FO(\))p FG(;)g FN(Cont)p FO(\()p FN(c)26930 40995
y Fz(n)p FB(+)p Fz(2)28674 40813 y FG(;)g FA(\244)p FG(;)p
30767 40813 V 638 w FO(\))p FG(;)g FN(Cont)p FO(\()p
FN(c)35595 40995 y Fz(n)p FB(+)p Fz(3)37339 40813 y FG(;)g
FA(F)p 39096 40813 V 436 w FO(\))p FI(g)7749 43104 y
FO(gdje)404 b(su)h FN(c)12436 43293 y Fz(i)13119 43104
y FO(imena)f(p)34 b(olja)405 b(p)34 b(o)-34 b(\267)-572
b(cetne)404 b(k)-34 b(on\257guracije.)9631 46134 y FL(T)-116
b(ranzicije)675 b(i)h(miro)-39 b(v)-77 b(anja:)1948 b
FO(za)588 b(sv)-67 b(aku)587 b(tranziciju)h(u)h FG(\261)633
b FO(Horno)-34 b(v)g(o)67 b(j)590 b(teoriji)7749 47639
y(do)34 b(da)67 b(jemo)334 b(o)34 b(dgo)-34 b(v)-67 b(ara)67
b(ju)-34 b(\266)-572 b(cu)334 b(klauzulu.)515 b(Gla)-34
b(v)-67 b(a)332 b(mo)-34 b(\267)-572 b(ze)299 b(\267)-572
b(citati)332 b(sim)-34 b(b)34 b(ol,)347 b(pisati)334
b(neki)e(no)-34 b(vi)7749 49145 y(i)403 b(p)34 b(omakn)-34
b(uti)406 b(se)e(ulijev)-34 b(o:)538 b FG(\261)46 b FO(\()p
FG(q)21945 49327 y FF(i)22321 49145 y FG(;)202 b(s)p
FO(\))337 b(=)f(\()p FG(q)26527 49327 y FF(j)27015 49145
y FG(;)202 b(s)28122 48705 y FE(0)28432 49145 y FG(;)g(L)p
FO(\).)539 b(Horno)-34 b(v)-67 b(a)404 b(form)-34 b(ula)405
b(je:)7749 51924 y FI(8)p FG(x;)202 b(y)43 b(;)202 b(z)53
b(;)202 b(s)12554 52106 y FB(1)13080 51924 y FG(;)g(s)14187
52106 y FB(2)14713 51924 y FO([)p FN(Adj)p FO(\()p FG(x;)g(y)43
b FO(\))p FI(^)p FN(Adj)q FO(\()p FG(y)g(;)202 b(z)53
b FO(\))p FI(^)p FN(Cont)r FO(\()p FG(x;)202 b(s)30444
52106 y FB(1)30970 51924 y FG(;)p 31582 51924 V 638 w
FO(\))p FI(^)p FN(Cont)q FO(\()p FG(y)43 b(;)202 b(s;)g(q)38964
52106 y FF(i)39341 51924 y FO(\))p FI(^)p FN(Cont)q FO(\()p
FG(z)53 b(;)202 b(s)45260 52106 y FB(2)45786 51924 y
FG(;)p 46397 51924 V 638 w FO(\))337 b(=)-202 b FI(\))9242
54760 y FO(=)g FI(\))337 b(9)p FG(x)12898 54260 y FE(0)13209
54760 y FG(;)202 b(y)14385 54260 y FE(0)14696 54760 y
FG(;)g(z)15852 54260 y FE(0)16162 54760 y FO(\()p FN(Adj)q
FO(\()p FG(x)19555 54260 y FE(0)19866 54760 y FG(;)g(y)21042
54260 y FE(0)21353 54760 y FO(\))269 b FI(^)h FN(Adj)p
FO(\()p FG(y)26036 54260 y FE(0)26348 54760 y FG(;)202
b(z)27504 54260 y FE(0)27814 54760 y FO(\))270 b FI(^)g
FN(Cont)p FO(\()p FG(x)33241 54260 y FE(0)33552 54760
y FG(;)202 b(s)34659 54942 y FB(1)35185 54760 y FG(;)g(q)36265
54942 y FF(j)36751 54760 y FO(\))270 b FI(^)f FN(Cont)q
FO(\()p FG(y)42122 54260 y FE(0)42434 54760 y FG(;)202
b(s)43541 54260 y FE(0)43851 54760 y FG(;)p 44463 54760
V 638 w FO(\))p FI(^)14294 57108 y(^)p FN(Cont)q FO(\()p
FG(z)18635 56607 y FE(0)18946 57108 y FG(;)g(s)20053
57290 y FB(2)20578 57108 y FG(;)p 21190 57108 V 639 w
FO(\))269 b FI(^)h FN(Bel)o FO(\()p FG(x;)202 b(x)27404
56607 y FE(0)27714 57108 y FO(\))270 b FI(^)f FN(Bel)p
FO(\()p FG(y)43 b(;)202 b(y)33453 56607 y FE(0)33765
57108 y FO(\))270 b FI(^)f FN(Bel)p FO(\()p FG(z)53 b(;)202
b(z)39464 56607 y FE(0)39774 57108 y FO(\)\)])7749 59418
y(Sli)-34 b(\267)-572 b(cna)404 b(se)g(form)-34 b(ula)404
b(dobije)h(za)f FG(\261)46 b FO(\()p FG(q)23935 59600
y FF(i)24311 59418 y FG(;)202 b(s)p FO(\))337 b(=)f(\()p
FG(q)28517 59600 y FF(j)29005 59418 y FG(;)202 b(s)30112
58978 y FE(0)30422 59418 y FG(;)g(R)9 b FO(\).)9631 62448
y(Sljede)-34 b(\266)-572 b(ce)356 b(treba)h(osigurati)f(da)h(netakn)-34
b(uta)359 b(p)34 b(olja)356 b(ostan)-34 b(u)358 b(onakv)-67
b(a)357 b(k)-67 b(akv)g(a)355 b(su)i(bila.)7749 63953
y(Kao)404 b(i)f(prije,)h(grupiramo)g(p)34 b(o)405 b(tri)e(p)34
b(olja)405 b(i)e(osta)-34 b(vljamo)406 b(ih)e(nepromjenjenima:)7749
66733 y FI(8)p FG(x;)202 b(y)43 b(;)202 b(z)53 b(;)202
b(s)12554 66915 y FB(1)13080 66733 y FG(;)g(s)14187 66915
y FB(2)14713 66733 y FG(;)g(s)15820 66915 y FB(3)16345
66733 y FO([)p FN(Adj)q FO(\()p FG(x;)g(y)43 b FO(\))p
FI(^)p FN(Adj)q FO(\()p FG(y)g(;)202 b(z)53 b FO(\))p
FI(^)p FN(Cont)r FO(\()p FG(x;)202 b(s)32077 66915 y
FB(1)32603 66733 y FG(;)p 33214 66733 V 638 w FO(\))p
FI(^)p FN(Cont)q FO(\()p FG(y)43 b(;)202 b(s)39517 66915
y FB(2)40044 66733 y FG(;)p 40655 66733 V 638 w FO(\))p
FI(^)p FN(Cont)q FO(\()p FG(z)53 b(;)202 b(s)46938 66915
y FB(3)47464 66733 y FG(;)p 48075 66733 V 638 w FO(\))13603
69569 y(=)-202 b FI(\))337 b(9)p FG(x)17259 69068 y FE(0)17569
69569 y FG(;)202 b(y)18745 69068 y FE(0)19056 69569 y
FG(;)g(z)20212 69068 y FE(0)20523 69569 y FO(\()p FN(Adj)q
FO(\()p FG(x)23916 69068 y FE(0)24226 69569 y FG(;)g(y)25402
69068 y FE(0)25713 69569 y FO(\))270 b FI(^)g FN(Adj)p
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b(z)31865 69068 y FE(0)32175 69569 y FO(\))270 b FI(^)f
FN(Cont)q FO(\()p FG(y)37546 69068 y FE(0)37858 69569
y FG(;)202 b(s)38965 69751 y FB(2)39490 69569 y FG(;)p
40102 69569 V 638 w FO(\))p FI(^)18429 71916 y(^)p FN(Bel)o
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%%Page: 41 41
TeXDict begin HPSdict begin 41 40 bop 4317 7181 a FO(Zatim,)370
b(\267)-572 b(cuv)-67 b(amo)404 b(lijev)-34 b(o)403 b(kra)67
b(jnje)405 b(p)34 b(olje)404 b FG(x)g FO(k)-67 b(akv)-34
b(o)403 b(je)h(bilo:)5669 9995 y FI(8)p FG(x;)202 b(y)43
b FO([)p FN(Cont)p FO(\()p FG(x;)202 b FA(F)p FG(;)p
14452 9995 364 45 v 638 w FO(\))270 b FI(^)f FN(Adj)q
FO(\()p FG(x;)202 b(y)43 b FO(\))338 b(=)-202 b FI(\))336
b(9)p FG(x)25195 9495 y FE(0)25506 9995 y FN(Cont)p FO(\()p
FG(x)29114 9495 y FE(0)29425 9995 y FG(;)202 b FA(F)p
FG(;)p 31720 9995 V 638 w FO(\))269 b FI(^)h FN(Bel)o
FO(\()p FG(x;)202 b(x)37934 9495 y FE(0)38244 9995 y
FO(\)])4317 12839 y(Desnom)405 b(kra)67 b(ju)404 b FG(y)448
b FO(za)404 b(p)34 b(otreb)g(e)404 b(ra)-34 b(\267)-572
b(cunanja)405 b(do)34 b(da)67 b(jemo)405 b(:)3804 15653
y FI(8)p FG(x;)202 b(y)43 b FO([)p FN(Adj)q FO(\()p FG(x;)202
b(y)43 b FO(\))270 b FI(^)f FN(Cont)q FO(\()p FG(y)43
b(;)202 b FA(F)p FG(;)p 18448 15653 V 639 w FO(\))337
b(=)-202 b FI(\))336 b(9)p FG(y)23219 15153 y FE(0)23531
15653 y FG(;)202 b(z)24687 15153 y FE(0)24997 15653 y
FN(Cont)q FO(\()p FG(y)28550 15153 y FE(0)28861 15653
y FG(;)g FA(\244)p FG(;)p 30954 15653 V 638 w FO(\))270
b FI(^)f FN(Cont)q FO(\()p FG(z)36669 15153 y FE(0)36980
15653 y FG(;)202 b FA(F)p FG(;)p 39274 15653 V 637 w
FO(\))p FI(^)16205 18558 y(^)p FN(Bel)p FO(\()p FG(y)43
b(;)202 b(y)20934 18057 y FE(0)21246 18558 y FO(\))270
b FI(^)f FN(Adj)q FO(\()p FG(y)25930 18057 y FE(0)26241
18558 y FG(;)202 b(z)27397 18057 y FE(0)27708 18558 y
FO(\)])4317 20919 y(Jo)-64 b(\267)-542 b(s)404 b(je)g(jedna)h(Horno)-34
b(v)-67 b(a)405 b(klauzula)e(v)-67 b(a)-34 b(\267)-572
b(zna,)404 b(ona)g(k)-34 b(o)67 b(ja)405 b(dr)-34 b(\267)-572
b(zi)404 b(sv)-67 b(a)403 b(p)34 b(olja)405 b(na)f(okupu:)6939
23733 y FI(8)p FG(x;)202 b(x)9537 23232 y FE(0)9847 23733
y FG(;)g(y)43 b(;)202 b(y)12199 23232 y FE(0)12511 23733
y FO([)p FN(Adj)p FO(\()p FG(x;)g(y)43 b FO(\))270 b
FI(^)g FN(Bel)o FO(\()p FG(x;)202 b(x)22796 23232 y FE(0)23106
23733 y FO(\))270 b FI(^)g FN(Bel)o FO(\()p FG(y)43 b(;)202
b(y)28845 23232 y FE(0)29157 23733 y FO(\))337 b(=)-202
b FI(\))337 b FN(Adj)p FO(\()p FG(x)35176 23232 y FE(0)35487
23733 y FG(;)202 b(y)36663 23232 y FE(0)36974 23733 y
FO(\)])2435 26748 y FL(T)-116 b(eorem)464 b(3)606 b FK(T)-93
b(uringov)336 b(str)-62 b(oj)336 b FG(M)469 b FK(staje)335
b(za)i(ulaz)e FG(w)370 b FK(ako)336 b(i)g(samo)g(ako)g(je)h
FN(Cont)p FO(\()p FG(x;)202 b(a;)g(q)41210 26945 y FF(f)41814
26748 y FO(\))2435 28253 y FK(za)309 b(neke)g FG(x)p
FK(,)334 b FG(a)310 b FK(i)f FG(q)10096 28450 y FF(f)11038
28253 y FI(2)337 b FG(Q)13141 28441 y FF(F)14232 28253
y FK(izve)-62 b(diva)276 b(\267)-589 b(cinjenic)-62 b(a)308
b(Hornove)h(te)-62 b(orije)307 b FG(H)98 b FO(\()p FG(M)65
b(;)202 b(w)33 b FO(\))p FK(,)334 b FG(H)98 b FO(\()p
FG(M)65 b(;)202 b(w)33 b FO(\))337 b FI(`)2435 29759
y FN(Cont)q FO(\()p FG(x;)202 b(a;)g(q)8304 29956 y FF(f)8908
29759 y FO(\))p FK(.)2435 32744 y(Dokaz.)537 b FO(Pro)-34
b(v)g(o)34 b(dimo)404 b(ga)g(induk)-34 b(cijom)405 b(u)g(oba)f(smjera.)
2435 34249 y(Prv)-34 b(o)294 b(pretp)34 b(osta)-34 b(vimo)296
b(da)f FG(M)426 b FO(sta)67 b(je)295 b(za)f(ulaz)h FG(w)33
b FO(.)501 b(Ak)-34 b(o)295 b(se)f(to)h(dogo)34 b(di)294
b(u)h(n)-34 b(ultom)296 b(k)-34 b(oraku)2435 35755 y(T)-101
b(uringo)-34 b(v)g(og)407 b(stro)67 b(ja,)407 b(zna)-34
b(\267)-572 b(ci)405 b(da)h(je)f(p)34 b(o)-34 b(\267)-572
b(cetno)406 b(stanje)g FG(q)27316 35937 y FB(0)28248
35755 y FO(ujedno)h(i)e(za)-34 b(vr)-64 b(\267)-542 b(sno,)405
b FG(q)38197 35937 y FB(0)39062 35755 y FI(2)339 b FG(Q)41167
35943 y FF(F)41949 35755 y FO(,)2435 37260 y(i)404 b
FG(H)98 b FO(\()p FG(M)65 b(;)202 b(w)33 b FO(\))404
b(tada)h(izv)-34 b(o)34 b(di)369 b(\267)-572 b(zeljen)-34
b(u)404 b FN(Cont)q FO(\()p FG(x;)202 b(a;)g(q)24514
37442 y FB(0)25039 37260 y FO(\).)2435 38766 y(Ak)-34
b(o)627 b(T)-101 b(uringo)-34 b(v)626 b(stro)67 b(j)628
b(sta)67 b(je)627 b(nak)-34 b(on)627 b FG(k)664 b FO(k)-34
b(orak)-67 b(a,)681 b(tada)626 b(je)h(za)-34 b(vr)-64
b(\267)-542 b(sna)626 b(k)-34 b(on\257guracija)2435 40271
y(opisana)351 b(retk)-34 b(om)351 b FG(r)11370 40468
y FF(k)12288 40271 y FO(tabloa,)362 b(sa)350 b(svim)g(pretho)34
b(dnim)351 b(k)-34 b(on\257guracijama)352 b(zabilje)-34
b(\267)-572 b(zenim)2435 41777 y(u)634 b(retcima)f FG(r)8899
41959 y FB(0)9425 41777 y FG(;)202 b(:)g(:)g(:)e(;)i(r)12665
41974 y FF(k)24 b FE(\241)p FB(1)14436 41777 y FO(.)1227
b(Pretp)34 b(osta)-34 b(vimo)633 b(da)h(Horno)-34 b(v)-67
b(a)634 b(teorija)f FG(H)98 b FO(\()p FG(M)65 b(;)202
b(w)33 b FO(\))633 b(sli-)2435 43282 y(jedi)463 b(k)-34
b(orak)463 b(p)34 b(o)463 b(k)-34 b(orak)462 b(T)-101
b(uringo)-34 b(v)464 b(stro)67 b(j)464 b(do)f(\()p FG(k)348
b FI(\241)308 b FO(1\))463 b(k)-34 b(orak)-67 b(a,)477
b(tj.)463 b(imamo)g(dok)-67 b(azane)2435 44788 y FN(Cont)q
FO(\()p FG(x;)202 b(a;)g(q)43 b FO(\))491 b(akk)-34 b(o)490
b(je)h(T)-101 b(uringo)-34 b(v)491 b(stro)67 b(j)491
b(u)g(stanju)i FG(q)43 b FO(,)512 b(njego)-34 b(v)-67
b(a)491 b(gla)-34 b(v)-67 b(a)490 b(iznad)h FG(x)456
b FO(\267)-572 b(cita)2435 46293 y(sim)-34 b(b)34 b(ol)493
b FG(a)p FO(,)514 b(i)493 b(imamo)f FN(Cont)q FO(\()p
FG(x;)202 b(a;)p 18152 46293 V 637 w FO(\))493 b(akk)-34
b(o)493 b(je)g(u)g(p)34 b(olju)493 b FG(x)g FO(zapisano)g
FG(a)p FO(,)514 b(za)492 b(sv)-67 b(a)493 b(p)34 b(olja)2435
47799 y(k)-34 b(o)67 b(je)405 b(gla)-34 b(v)-67 b(a)404
b(ne)370 b(\267)-572 b(cita)404 b(u)g(\()p FG(k)308 b
FI(\241)269 b FO(1\))405 b(k)-34 b(oraku.)2435 49304
y(Moramo)586 b(p)34 b(ok)-67 b(azati)584 b(da)i(je)f(vjernost)h(zadr)
-34 b(\267)-572 b(zana)585 b(i)g(nak)-34 b(on)586 b(izvr)-64
b(\267)-542 b(senja)585 b FG(k)38 b FO(tog)585 b(k)-34
b(orak)-67 b(a)2435 50810 y(ra)-34 b(\267)-572 b(cunanja)383
b(stro)67 b(ja.)531 b(T)-101 b(ak)-34 b(o)382 b(i)f(jest:)527
b(ak)-34 b(o)382 b(je,)j(na)c(primjer,)386 b FG(k)38
b FO(-ti)381 b(k)-34 b(orak)381 b(bio)g FG(\261)46 b
FO(\()p FG(q)37657 51007 y FF(k)24 b FE(\241)p FB(1)39428
50810 y FG(;)202 b(s)p FO(\))337 b(=)2435 52315 y(\()p
FG(q)3447 52512 y FF(k)4017 52315 y FG(;)202 b(s)5124
51875 y FE(0)5434 52315 y FG(;)g(R)9 b FO(\))547 b(tada)g(imamo)g
(Horno)-34 b(vu)547 b(form)-34 b(ulu)547 b(k)-34 b(o)67
b(ja)547 b(ta)67 b(j)547 b(doga)p 32307 51701 364 53
v(da)67 b(j)548 b(opisuje,)583 b(uz)546 b(sv)-34 b(e)2435
53820 y(form)g(ule)646 b(za)f(o)34 b(dr)-34 b(\267)-572
b(za)-34 b(v)-67 b(anje)645 b(preostalih)g(p)34 b(olja.)1262
b(T)-101 b(ada,)706 b(ak)-34 b(o)646 b(je)f FG(q)33478
54017 y FF(k)34785 53820 y FI(2)739 b FG(Q)37290 54008
y FF(F)38717 53820 y FO(imamo)2435 55326 y FN(Cont)q
FO(\()p FG(x;)202 b(a;)g(q)8304 55523 y FF(k)8872 55326
y FO(\))404 b(izv)-34 b(edivu)404 b(u)g FG(H)98 b FO(\()p
FG(M)65 b(;)202 b(w)33 b FO(\).)4317 58367 y(Nek)-67
b(a)534 b(je)h FG(H)98 b FO(\()p FG(M)65 b(;)202 b(w)33
b FO(\))555 b FI(`)g FN(Cont)p FO(\()p FG(x;)202 b(a;)g(q)21370
58564 y FF(f)21975 58367 y FO(\))535 b(za)g(nek)-34 b(e)535
b FG(x)p FO(,)567 b FG(a)534 b FO(i)h FG(q)31738 58564
y FF(f)32898 58367 y FI(2)555 b FG(Q)35219 58555 y FF(F)36001
58367 y FO(.)37404 58061 y(\267)37269 58367 y(Cinjenicu)2435
59873 y FN(Cont)q FO(\()p FG(x;)202 b(a;)g(q)8304 60070
y FF(f)8908 59873 y FO(\))465 b(mogli)e(smo)i(dobiti)f(iz)g(nek)-34
b(e)464 b(o)34 b(d)464 b(klauzula)g(k)-34 b(o)67 b(je)464
b(opisuju)i(tranzicije,)2435 61378 y(dakle)333 b(nak)-34
b(on)335 b(p)34 b(omak)-67 b(a)333 b(gla)-34 b(v)g(e)333
b(lijev)-34 b(o)333 b(ili)g(desno,)348 b(nad)334 b(p)34
b(olje)334 b FG(x)p FO(,)347 b(gdje)334 b(je)f(gla)-34
b(v)-67 b(a)333 b(napisala)2435 62884 y FG(a)371 b FO(i)g(stanje)i(T)
-101 b(uringo)-34 b(v)g(og)372 b(stro)67 b(ja)373 b(p)34
b(ostalo)371 b FG(q)22134 63081 y FF(f)22739 62884 y
FO(.)528 b(Nek)-67 b(a)370 b(je)i(to)g(bila,)377 b(na)372
b(primjer,)377 b(form)-34 b(ula)2435 64389 y(za)390 b(p)34
b(omak)391 b(udesno.)535 b(T)-101 b(ada)391 b(je)f FN(Cont)q
FO(\()p FG(x;)202 b(a;)g(q)22662 64586 y FF(f)23266 64389
y FO(\))391 b(dobiv)-34 b(ena)391 b(k)-34 b(onzumiranjem)358
b(\267)-572 b(cinjenice)2435 65894 y FN(Cont)q FO(\()p
FG(x)6044 65455 y FE(0)6354 65894 y FG(;)202 b(a)7534
65455 y FE(0)7844 65894 y FG(;)g(q)8967 65455 y FE(0)9278
65894 y FO(\),)525 b(gdje)501 b(je)g FG(x)15403 65455
y FE(0)16214 65894 y FO(p)34 b(olje)501 b(lijev)-34 b(o)500
b(iznad)h(u)g(tablou.)829 b(Konzumirane)501 b(su)g(jo)-64
b(\267)-542 b(s)2402 67400 y(\267)-572 b(cinjenice)546
b(k)-34 b(o)67 b(je)548 b(go)-34 b(v)g(ore)547 b(o)g(p)34
b(oljima)548 b(lijev)-34 b(o)547 b(i)g(desno)h(o)34 b(d)547
b FG(x)30185 66960 y FE(0)30495 67400 y FO(,)583 b(a)547
b(proizv)-34 b(edene)547 b(one)h(o)2435 68905 y(p)34
b(oljima)538 b(isp)34 b(o)g(d)538 b(njih,)572 b(u)538
b(sljede)-34 b(\266)-572 b(cem)538 b(retku)g(tabloa.)940
b(Sv)-34 b(e)538 b(ostale)504 b(\267)-572 b(cinjenice)537
b(su)i(ne-)2435 70411 y(promjenjene.)504 b(Kak)-34 b(o)297
b(inicijalizacijsk)-34 b(e)296 b(Horno)-34 b(v)g(e)297
b(klauzule)g(o)34 b(dgo)-34 b(v)-67 b(ara)67 b(ju)298
b(inicijalnom)2435 71916 y(stanju)406 b(T)-101 b(uringo)-34
b(v)g(og)405 b(stro)67 b(ja,)405 b(op)34 b(et)405 b(induk)-34
b(cijom)404 b(slijedi)g(dok)-67 b(az.)538 b FA(\244)21755
74956 y FO(41)p eop end end
%%Page: 42 42
TeXDict begin HPSdict begin 42 41 bop 7749 7181 a FL(Korolar)464
b(1)606 b FK(Pr)-62 b(oblem)309 b(izvo)-62 b(d)62 b(ljivosti)305
b(za)k(e)-62 b(gzistencijalne)306 b(Hornove)i(klauzule)f(b)-62
b(ez)308 b(funk-)7749 8687 y(cijskih)431 b(simb)-62 b(ola,)431
b(je)i(ne)-62 b(o)g(d)62 b(lu)-31 b(\267)-589 b(civ.)7749
11521 y FL(Korolar)464 b(2)606 b FK(Pr)-62 b(oblem)363
b(tajnosti)f FI(S)23950 11718 y FF(siz)37 b(e)p FB(=)p
FF(k)27282 11521 y FK(\(te)-62 b(or)g(em)363 b(2\),)377
b(za)456 b FO(k)p FK(-ove)362 b(ve)-31 b(\266)-589 b(ce)363
b(o)-62 b(d)363 b(neke)g(male)7749 13026 y(vrije)-62
b(dnosti,)430 b(je)j(ne)-62 b(o)g(d)62 b(lu)-31 b(\267)-589
b(civ.)9631 15860 y FO(Za)509 b(o)-34 b(vu)511 b(k)-34
b(onstruk)g(ciju)511 b FG(k)38 b FO(,)537 b(gornja)510
b(ograda)h(v)-34 b(eli)g(\267)-572 b(cine)509 b(p)34
b(oruk)-34 b(e,)536 b(nije)510 b(v)-34 b(e)g(\266)-572
b(ci)509 b(o)34 b(d)510 b(30,)7685 17365 y(\267)-542
b(sto)563 b(je)g(v)-34 b(eli)g(\267)-572 b(cina)562 b(na)67
b(jv)-34 b(e)g(\266)-572 b(ce)564 b(form)-34 b(ule)563
b(k)-34 b(o)67 b(ja)564 b(se)f(p)34 b(o)67 b(ja)-34 b(vljuje.)1016
b(Rezultat)564 b(bi)f(se)g(mogao)7749 18871 y(p)34 b(opra)-34
b(viti)404 b(pa)-34 b(\267)-572 b(zljivijim)404 b(o)34
b(dabirom)404 b(predik)-67 b(ata.)27068 74956 y(42)p
eop end end
%%Page: 43 43
TeXDict begin HPSdict begin 43 42 bop 2435 15596 a FJ(P)-72
b(ogla)g(vlje)864 b(4)2435 21243 y FM(Mo)86 b(del)1033
b(niti)2435 27289 y FO(Jednak)-34 b(o)297 b(in)-34 b(tuitiv)-67
b(an)297 b(k)-67 b(ao)296 b(transformacije)h(skup)34
b(o)-34 b(v)-67 b(a,)317 b(ili)262 b(\267)-572 b(cak)295
b(i)h(in)-34 b(tuitivniji,)319 b(jednak)-34 b(og)2435
28795 y(niv)g(oa)318 b(apstrak)-34 b(cije,)335 b(o)-34
b(v)-67 b(a)67 b(j)318 b(formalizam)f(n)-34 b(udi)318
b(vrlo)f(ugo)34 b(dn)-34 b(u)319 b(vizualn)-34 b(u)318
b(predo)34 b(d)-34 b(\267)-572 b(zbu,)335 b(jer)2435
30300 y(predsta)-34 b(vlja)405 b(protok)-34 b(ole)405
b(u)f(obliku)g(ozna)-34 b(\267)-572 b(cenih)404 b(grafo)-34
b(v)-67 b(a.)4317 33424 y(Sp)34 b(eci\257)-34 b(\267)-572
b(cni)405 b(grafo)-34 b(vi)405 b(k)-34 b(o)67 b(ji)405
b(opisuju)h(izvr)-64 b(\267)-542 b(senja)404 b(protok)-34
b(ola)406 b(zo)-34 b(vu)404 b(se)h FK(snop)-62 b(ovi)526
b FO(\()p FK(bun-)2435 34929 y(d)62 b(les)99 b FO(\).)538
b(Sv)-67 b(aki)403 b(snop)h(reprezen)-34 b(tira)403 b(uh)-34
b(v)-67 b(a)-34 b(\266)-572 b(ceni)404 b(tren)-34 b(utak)404
b(izvr)-64 b(\267)-542 b(senja)403 b(protok)-34 b(ola,)404
b(jedn)-34 b(u)2435 36435 y(mogu)g(\266)-572 b(cu)458
b(rundu)g(protok)-34 b(ola,)470 b(ili)456 b(njen)h(pre\257ks,)470
b(egzekuciju)456 b(prvih)h(nek)-34 b(olik)g(o)456 b(k)-34
b(orak)-67 b(a)2435 37940 y(protok)-34 b(ola.)555 b(U)409
b(slu)-34 b(\267)-572 b(ca)67 b(ju)410 b(k)-34 b(orektno)409
b(oba)-34 b(vljenog)410 b(protok)-34 b(ola,)411 b(onog)f(gdje)g(se)f
(uljez)g(nije)2435 39446 y(umje)-64 b(\267)-542 b(sao,)358
b(i)345 b(gdje)h(su)g(sudionici)f(protok)-34 b(ola)346
b(o)34 b(digrali)344 b(sv)-34 b(o)67 b(je)346 b(uloge)g(p)34
b(o)345 b(propisima)h(pro-)2435 40951 y(tok)-34 b(ola,)582
b(dobijamo)547 b(shem)-34 b(u)548 b(sli)-34 b(\267)-572
b(cn)-34 b(u)546 b(neformalnim)h(sli)-34 b(\267)-572
b(cicama)545 b(protok)-34 b(ola.)966 b(Primjer)2435 42457
y(snopa)456 b(k)-34 b(o)67 b(ji)455 b(predsta)-34 b(vlja)456
b(k)-34 b(orektn)g(u)456 b(rundu)g(Dolev-Y)-101 b(ao)454
b(protok)-34 b(ola)455 b(je)g(dan)h(na)f(slici)2435 43962
y(4.1.)539 b(Sv)-67 b(ak)g(a)403 b(p)34 b(o)67 b(jedina)405
b(rola)f(opisana)h(je)f(grafom)g(k)-34 b(o)67 b(ji)405
b(se)f(naziv)-67 b(a)403 b FK(nit)519 b FO(\()p FK(str)-62
b(and)125 b FO(\).)4317 47086 y(Mo)34 b(del)358 b(niti)g(je)g
(originalno)g(diza)67 b(jniran)359 b(za)f(dok)-67 b(aziv)g(anje)357
b(k)-34 b(orektnosti)359 b(protok)-34 b(ola,)2435 48591
y(i)538 b(to)g(ru)-34 b(\267)-572 b(cno,)572 b(za)538
b(razliku)f(o)34 b(d)538 b(transformacija)h(m)-34 b(ultiskup)34
b(o)-34 b(v)-67 b(a)539 b(gdje)f(je)g(o)34 b(d)538 b(p)34
b(o)-34 b(\267)-572 b(cetk)-67 b(a)2435 50096 y(na)438
b(um)-34 b(u)438 b(bio)g(v)-34 b(eri\257k)-67 b(ator)436
b(dok)-67 b(aza)437 b(LLF.)f(Prvi)h(put)h(se)f(p)34 b(o)67
b(ja)-34 b(vio)438 b(u)404 b(\267)-572 b(clanku)437 b([THG99])2435
51602 y(\(o)34 b(dnosno,)427 b(go)34 b(din)-34 b(u)422
b(dana)g(prije)f(ob)67 b(ja)-34 b(vljiv)-67 b(anja)422
b(mo)34 b(dela)421 b(transformacija)h(m)-34 b(ultisku-)2435
53107 y(p)34 b(ov)-67 b(a\).)667 b(F)-101 b(ormalizam)447
b(je)g(usk)-34 b(oro)447 b(dobio)h(v)-34 b(eri\257k)-67
b(ator)446 b(mo)34 b(dela)447 b FK(A)-31 b(thenu)93 b
FO(:)623 b(D.)446 b(Song,)458 b(u)2435 54613 y([Son99)q(].)2435
59075 y FH(4.1)1793 b(De\257nicije)2435 62000 y FL(P)-39
b(oruk)g(e)2435 64507 y FK(Poruke)599 b FO(su)510 b(izgra)p
11238 63893 364 53 v(dene)f(induktivno)h(o)34 b(d)509
b(atoma.)855 b(Sv)-34 b(e)509 b(p)34 b(oruk)-34 b(e)510
b(su)f(termi)g(k)-34 b(o)67 b(ji)510 b(pri-)2435 66012
y(pada)67 b(ju)406 b(skupu)f FL(M)p FO(,)340 b(\267)-542
b(sto)405 b(je)f(slob)34 b(o)g(dna)405 b(algebra)f(terama)g(dobiv)-34
b(ena)405 b(iz:)4253 68964 y FI(\262)607 b FL(A)p FO(,)403
b(skupa)i(atomarnih)g(tekst)f(terama;)4253 71916 y FI(\262)607
b FL(K)p FO(,)403 b(skupa)i(klju)-34 b(\267)-572 b(cev)-67
b(a)403 b(za)h(enkrip)34 b(ciju;)21755 74956 y(43)p eop
end end
%%Page: 44 44
TeXDict begin HPSdict begin 44 43 bop 9567 7181 a FI(\262)606
b FL(K)11872 6741 y FE(\241)p Fj(1)13201 7181 y FO(,)404
b(skupa)h(klju)-34 b(\267)-572 b(cev)-67 b(a)403 b(za)h(dekrip)34
b(ciju.)538 b(Bijektivno)403 b(preslik)-67 b(a)-34 b(v)-67
b(anje)25238 9742 y FN(inv)353 b FO(:)337 b FL(K)f FI(!)h
FL(K)31811 9242 y FE(\241)p Fj(1)10779 12303 y FO(pridru)-34
b(\267)-572 b(zuje)373 b(enkrip)34 b(cijski)371 b(klju)-34
b(\267)-572 b(c)373 b(njego)-34 b(v)g(om)374 b(dekrip)34
b(cijsk)-34 b(om)372 b(paru;)383 b FG(inv)43 b FO(\()p
FG(K)87 b FO(\))372 b(je,)10715 13808 y(\267)-542 b(sto)405
b(je)f(uobi)-34 b(\267)-572 b(ca)67 b(jeno,)405 b(ozna)-34
b(\267)-572 b(cen)404 b FG(K)26178 13368 y FE(\241)p
FB(1)9567 16256 y FI(\262)606 b FL(N)p FO(,)404 b(skupa)g(imena)g
(agenata;)7749 18622 y(te)g(sljede)-34 b(\266)-572 b(cih)404
b(k)-34 b(onstruk)-67 b(ata:)9567 21294 y FI(\262)606
b FO(enkrip)34 b(cije:)537 b(ak)-34 b(o)405 b(su)f FG(m)337
b FI(2)g FL(M)p FO(,)404 b(i)g FG(k)374 b FI(2)337 b
FL(K)404 b FO(onda)h(je)f FI(f)p FG(m)p FI(g)36137 21491
y FF(k)37043 21294 y FI(2)337 b FL(M)p FO(;)9567 23741
y FI(\262)606 b FO(spariv)-67 b(anja:)539 b(ak)-34 b(o)404
b(su)h FG(m)21894 23923 y FB(1)22420 23741 y FG(;)202
b(m)24023 23923 y FB(2)24885 23741 y FI(2)337 b FL(M)404
b FO(onda)h(je)f(\()p FG(m)33568 23923 y FB(1)34095 23741
y FG(;)202 b(m)35698 23923 y FB(2)36223 23741 y FO(\))338
b FI(2)e FL(M)9631 26413 y FO(Enkrip)34 b(cija)268 b(i)h(spariv)-67
b(anje)270 b(su)g(injektivni,)231 b(\267)-542 b(sto)270
b(omogu)-34 b(\266)-572 b(cuje)271 b(ni)-34 b(\267)-572
b(ze)269 b(de\257niran)-34 b(u)270 b(relaciju)7749 27918
y("biti)404 b(p)34 b(o)g(dterm".)7749 29424 y(Svi)269
b(skup)34 b(o)-34 b(vi)269 b FL(A)p FO(,)296 b FL(K)p
FO(,)g FL(K)18490 28984 y FE(\241)p Fj(1)19819 29424
y FO(,)g FL(N)269 b FO(su)h(me)p 25043 28810 364 53 v(dusobno)h
(disjunktni,)298 b(osim)269 b(u)h(slu)-34 b(\267)-572
b(ca)67 b(ju)270 b(simetri)-34 b(\267)-572 b(cne)7749
30929 y(enkrip)34 b(cije)459 b(k)-67 b(ada)460 b(se)g
FL(K)g FO(i)f FL(K)21201 30489 y FE(\241)p Fj(1)22991
30929 y FO(p)34 b(o)g(dudara)67 b(ju,)476 b(i)460 b FN(inv)476
b FO(je)461 b(iden)-34 b(titeta.)708 b(T)-101 b(ak)-34
b(o)p 43066 30316 V(der,)474 b(slik)-34 b(e)7749 32435
y(enkrip)34 b(cije)409 b(i)h(spariv)-67 b(anja)411 b(su)g(me)p
23241 31821 V(dusobno)h(disjunktne,)i(i)c(disjunktne)i(sa)f(sv)-67
b(akim)409 b(o)34 b(d)7749 33940 y FL(A)p FO(,)403 b
FL(N)p FO(,)h FL(K)p FO(,)f FL(K)14301 33500 y FE(\241)p
Fj(1)15630 33940 y FO(.)7749 35446 y(Time)576 b(je)h(jezik)e(p)34
b(oruk)-67 b(a)576 b FK(tipizir)-62 b(an)p FO(.)1054
b(Tipiziranje)576 b(p)34 b(oruk)-67 b(a)576 b(spre)-34
b(\267)-572 b(ca)-34 b(v)-67 b(a,)619 b(na)577 b(primjer,)7749
36951 y(zamjen)-34 b(u)468 b(imena)f(za)g(sol,)482 b(i)467
b(time)g(ne)g(otkriv)-67 b(a)466 b(klasu)h(napada)h(k)-34
b(o)67 b(je)468 b(se)f(na)g(to)h(oslan-)7749 38457 y(ja)67
b(ju)585 b({)g FK(nap)-62 b(ade)597 b(gr)-62 b(e)g(\267)-558
b(ske)598 b(tipizacije)p FO(.)1075 b(T)-101 b(o)584 b(su)h(napadi)g
(pri)f(k)-34 b(o)67 b(jima)585 b(uljezu)f(usp)67 b(jev)-67
b(a)7749 39962 y(p)34 b(o)g(dv)-67 b(aliti)445 b(p)34
b(o)-64 b(\267)-542 b(stenom)447 b(sudioniku)g(falsi\257ciran)-34
b(u)447 b(p)34 b(oruku,)457 b(takvu)446 b(da)h(je)f(sol)g(zamjen-)7749
41468 y(jena)485 b(nek)-34 b(om)484 b(p)34 b(oruk)-34
b(om)485 b(drugog)h(tipa.)780 b(Tipiziranje)484 b(p)34
b(oruk)-67 b(a)484 b(je)h(prednost,)505 b(napadi)7749
42973 y(gre)-64 b(\267)-542 b(sk)-34 b(e)505 b(tipizacije)g(u)h(v)-34
b(e)g(\266)-572 b(cini)505 b(slu)-34 b(\267)-572 b(ca)67
b(jev)-67 b(a)506 b(nisu)g(realni,)530 b(na)67 b(j)-34
b(\267)-572 b(ce)-64 b(\267)-542 b(s)-34 b(\266)-572
b(ce)506 b(ih)g(se)f(spre)-34 b(\267)-572 b(ca)-34 b(v)-67
b(a)505 b(pri)7749 44478 y(implemen)-34 b(taciji.)594
b(No)422 b(ipak,)427 b(p)34 b(osto)67 b(je)423 b(takvi)g(napadi)g(na)g
(k)-34 b(o)67 b(je)423 b(implemen)-34 b(tacije)423 b(nisu)7749
45984 y(im)-34 b(une.)7749 47489 y(Un)g(utar)540 b(opisanih)g(p)34
b(osta)-34 b(vki,)573 b(nek)-34 b(e)539 b(su)h(zloup)34
b(otreb)g(e)539 b(sprije)-34 b(\267)-572 b(cene,)572
b(druge)540 b(nisu.)944 b(U)7749 48995 y(o)-34 b(v)g(om)389
b(mo)34 b(delu)389 b(nije)g(o)34 b(dre)p 20089 48381
V(deno)389 b(je)325 b(\267)-542 b(sto)389 b(bi)g(trebala)g(biti)g(svje)
-34 b(\267)-572 b(za)389 b(vrijednost,)j(k)-67 b(ak)-34
b(o)388 b(ne-)7749 50500 y(mamo)531 b(sp)34 b(ecijalni)531
b(tip)h(soli,)563 b(pa)532 b(uljez)f(mo)-34 b(\267)-572
b(ze)531 b(usp)67 b(je)-64 b(\267)-542 b(sno)533 b(p)34
b(o)g(dmetn)-34 b(uti)534 b(za)d(sol)g(neku)7749 52006
y(drugu)405 b(p)34 b(oruku,)404 b(k)-67 b(ao)340 b(\267)-542
b(sto)404 b(su)h(enkrip)34 b(cija)403 b(ili)g(par.)7749
53511 y(Sp)34 b(omen)-34 b(uti)271 b(tip)34 b(o)-34 b(vi)269
b(su)h(preuzeti)f(iz)g([THG99],)296 b(no)236 b(\267)-572
b(clanak)269 b(tak)-34 b(o)p 37112 52898 V(der)270 b(osta)-34
b(vlja)270 b(mogu)-34 b(\266)-572 b(cnost)7749 55017
y(slob)34 b(o)g(dnog)270 b(o)34 b(dabira)269 b(na)-34
b(\267)-572 b(cina)270 b(gradnje)g(p)34 b(oruk)-34 b(e,)296
b(i)269 b(njenih)h(tip)34 b(o)-34 b(v)-67 b(a,)296 b(za)-34
b(visno)270 b(o)f(up)34 b(otrebi.)9631 58028 y(Enkrip)g(cije)288
b(su)i(mo)34 b(delirane)289 b(uz)g(pretp)34 b(osta)-34
b(vku)291 b(tak)-34 b(ozv)-67 b(ane)289 b(slob)34 b(o)g(dne)290
b(enkrip)34 b(cije,)7749 59533 y(naime)404 b(sp)34 b(omen)-34
b(ute)405 b(injektivnosti:)17396 62094 y FI(f)p FG(m)p
FI(g)19672 62291 y FF(k)20578 62094 y FO(=)337 b FI(f)p
FG(m)23528 61593 y FE(0)23838 62094 y FI(g)24444 62298
y FF(k)24958 62045 y FD(0)25985 62094 y FO(=)-202 b FI(\))673
b FG(m)337 b FO(=)g FG(m)32356 61593 y FE(0)33273 62094
y FI(^)606 b FG(k)375 b FO(=)336 b FG(k)37641 61593 y
FE(0)9631 64655 y FO(De\257nirana)404 b(je)g(relacija)f
FK(biti)433 b(p)-62 b(o)g(dterm)p FO(,)402 b FI(v)p FO(,)h(na)i(skupu)g
(p)34 b(oruk)-67 b(a)404 b FL(M)p FO(:)9567 67021 y FI(\262)606
b FG(m)337 b FI(v)f FG(a)404 b FO(ak)-34 b(o)404 b FG(m)337
b FO(=)g FG(a)404 b FO(za)f FG(a)337 b FI(2)g FG(A)9567
69469 y FI(\262)606 b FG(m)337 b FI(v)f FG(k)443 b FO(ak)-34
b(o)404 b FG(m)337 b FO(=)f FG(k)443 b FO(za)403 b FG(k)375
b FI(2)337 b FG(K)9567 71916 y FI(\262)606 b FG(m)337
b FI(v)f(f)p FG(m)15129 72098 y FB(1)15656 71916 y FI(g)16262
72113 y FF(k)17235 71916 y FO(ak)-34 b(o)404 b FG(m)337
b FI(v)f FG(m)23201 72098 y FB(1)24131 71916 y FO(ili)403
b FG(m)337 b FO(=)g FI(f)p FG(m)29896 72098 y FB(1)30422
71916 y FI(g)31028 72113 y FF(k)27068 74956 y FO(44)p
eop end end
%%Page: 45 45
TeXDict begin HPSdict begin 45 44 bop 4253 7181 a FI(\262)607
b FG(m)337 b FI(v)f FO(\()p FG(m)9681 7363 y FB(1)10207
7181 y FG(;)202 b(m)11810 7363 y FB(2)12336 7181 y FO(\))405
b(ak)-34 b(o)404 b FG(m)337 b FI(v)f FG(m)19178 7363
y FB(1)20108 7181 y FO(ili)404 b FG(m)337 b FI(v)f FG(m)25267
7363 y FB(2)4317 9717 y FO(Ov)-67 b(a)368 b(relacija)g(je)g(sredstv)-34
b(o)369 b(p)34 b(omo)-34 b(\266)-572 b(cu)369 b(k)-34
b(o)67 b(jeg)370 b(se)e(izra)-34 b(\267)-572 b(za)-34
b(v)-67 b(a)367 b(k)-67 b(auzalnost)369 b(un)-34 b(utar)371
b(niti)2435 11222 y(i)445 b(me)p 5027 10609 364 53 v(du)h(nitima)g(k)
-34 b(o)67 b(je)446 b(opisuju)h(protok)-34 b(ol.)663
b(P)-34 b(osebno,)456 b(ona)446 b(omogu)-34 b(\266)-572
b(cuje)446 b(da)g(se)f(izrazi)2435 12728 y(p)34 b(o)67
b(jam)405 b(uv)-34 b(o)p 8353 12114 V(denja)406 b(svje)-34
b(\267)-572 b(zih)404 b(vrijednosti,)g(k)-67 b(ao)339
b(\267)-542 b(sto)405 b(su)f(soli)g(i)g(no)-34 b(vi)404
b(klju)-34 b(\267)-572 b(cevi.)4317 15747 y(Na)67 b(j)-34
b(\267)-572 b(ce)-64 b(\267)-542 b(s)-34 b(\266)-572
b(ce)587 b(\266)-572 b(cemo)619 b(go)-34 b(v)g(oriti)621
b(o)f(p)34 b(oruk)-67 b(ama)620 b(s)h FK(pr)-62 b(e)g(dznakom)711
b FO(k)-34 b(o)67 b(je)621 b(predsta)-34 b(vlja)67 b(ju)2435
17252 y(sljede)-34 b(\266)-572 b(ce)404 b(doga)p 9605
16639 V(da)67 b(je:)5466 19788 y(+)p FG(m)404 b FO(ozna)-34
b(\267)-572 b(cuje)404 b FK(slanje)494 b FO(p)34 b(oruk)-34
b(e)404 b FG(m)p FO(;)5466 22323 y FI(\241)p FG(m)g FO(ozna)-34
b(\267)-572 b(cuje)404 b FK(primanje)494 b FO(p)34 b(oruk)-34
b(e)404 b FG(m)p FO(.)4317 24859 y(Nek)-67 b(a)333 b(je)g
FI(\247)p FL(M)g FO(skup)h(svih)f(doga)p 19129 24245
V(da)67 b(ja,)349 b(o)34 b(dnosno)334 b(p)34 b(oruk)-67
b(a)333 b(s)g(predznak)-34 b(om.)516 b(P)-34 b(oruk)g(e)2435
26364 y(s)483 b(predznak)-34 b(om)484 b(se)f(k)-34 b(oriste)483
b(za)g(ozna)-34 b(\267)-572 b(ca)-34 b(v)-67 b(anje)483
b(vrho)-34 b(v)-67 b(a)483 b(grafo)-34 b(v)-67 b(a)483
b(i)g(pam)-34 b(te)420 b(\267)-542 b(sto)483 b(se)g(do-)2435
27870 y(go)34 b(dilo)404 b(u)g(o)34 b(dre)p 9703 27256
V(denom)405 b(tren)-34 b(utku)405 b(izvr)-64 b(\267)-542
b(sa)-34 b(v)-67 b(anja)404 b(protok)-34 b(ola.)2435
31119 y FL(Nek)-39 b(e)465 b(de\257nicije)g(iz)f(teorije)h(grafo)-39
b(v)-77 b(a)2435 33424 y FO(Kao)322 b(\267)-542 b(sto)387
b(je)f(sp)34 b(omen)-34 b(uto,)391 b(k)-34 b(oncept)387
b(niti)g(k)-34 b(oristi)385 b(se)h(osno)-34 b(vnim)388
b(terminima)e(iz)f(teorije)2435 34930 y(grafo)-34 b(v)-67
b(a.)539 b(Nek)-34 b(olik)g(o)403 b(de\257nicija)i(k)-67
b(ao)403 b(p)34 b(o)g(dsjetnik:)4253 37465 y FI(\262)607
b FK(Usmjer)-62 b(eni)495 b(gr)-62 b(af)728 b FG(G)472
b FO(je)g(par)g(\()p FG(V)67 b(;)202 b FI(\241)-201 b(!)p
FO(\))472 b(gdje)h(je)f FG(V)742 b FO(neprazan)472 b(skup)439
b(\267)-572 b(ciji)471 b(se)h(el-)5466 38971 y(emen)-34
b(ti)519 b(zo)-34 b(vu)519 b(vrho)-34 b(vi,)548 b FI(\241)-202
b(!)p FO(,)547 b(p)34 b(o)g(dskup)520 b(o)34 b(d)519
b FG(V)616 b FI(\243)346 b FG(V)269 b FO(,)548 b(je)519
b(relacija)f FK(incidencije)5432 40476 y FO(\267)-572
b(ciji)380 b(se)i(elemen)-34 b(ti)381 b(zo)-34 b(vu)381
b(usmjerenim)h(brido)-34 b(vima.)531 b(Standardno,)388
b(ozna)-34 b(\267)-572 b(ca)-34 b(v)-67 b(amo)5466 41981
y(\()p FG(v)6525 42163 y FB(1)7050 41981 y FG(;)202 b(v)8177
42163 y FB(2)8702 41981 y FO(\))338 b FI(2\241)-203 b(!)405
b FO(k)-67 b(ao)403 b FG(v)15452 42163 y FB(1)16314 41981
y FI(\241)-202 b(!)337 b FG(v)19192 42163 y FB(2)19717
41981 y FO(.)4253 44517 y FI(\262)607 b FK(Bip)-62 b(artitni)562
b(gr)-62 b(af)801 b FO(je)545 b(usmjereni)h(graf)g FG(G)572
b FO(=)g(\()p FG(V)67 b(;)202 b FI(\241)-202 b(!)p FO(\))546
b(tak)-67 b(a)-34 b(v)545 b(da)h(su)g FG(V)39100 44699
y FB(1)40171 44517 y FO(i)f FG(V)41760 44699 y FB(2)5466
46022 y FO(disjunktni,)417 b FG(V)623 b FO(=)353 b FG(V)14878
46204 y FB(1)15680 46022 y FI([)276 b FG(V)17471 46204
y FB(2)17997 46022 y FO(,)416 b(i)e(ak)-34 b(o)414 b(je)g(\()p
FG(v)24115 46204 y FB(1)24641 46022 y FG(;)202 b(v)25768
46204 y FB(2)26293 46022 y FO(\))353 b FI(2\241)-202
b(!)414 b FO(tada)h FG(v)33651 46204 y FB(1)34530 46022
y FI(2)353 b FG(V)36398 46204 y FB(1)37338 46022 y FO(i)413
b FG(v)38676 46204 y FB(2)39555 46022 y FI(2)353 b FG(V)41423
46204 y FB(2)41949 46022 y FO(.)5466 47528 y(T)-101 b(ak)-67
b(a)-34 b(v)404 b(graf)g FG(G)g FO(ozna)-34 b(\267)-572
b(ca)-34 b(v)-67 b(amo)404 b FG(G)337 b FO(=)f(\()p FG(V)23334
47710 y FB(1)23860 47528 y FG(;)202 b(V)25106 47710 y
FB(2)25632 47528 y FG(;)g FI(\241)-202 b(!)p FO(\).)4253
50063 y FI(\262)607 b FK(Usmjer)-62 b(en)453 b(bigr)-62
b(af)681 b FO(je)426 b(tro)67 b(jk)-67 b(a)427 b(\()p
FG(S)s(;)202 b FI(\241)-202 b(!)p FG(;)202 b FO(=)-202
b FI(\))p FO(\))426 b(gdje)g(su)h(\()p FG(S)s(;)202 b
FI(\241)-202 b(!)p FO(\))426 b(i)g(\()p FG(S)s(;)202
b FO(=)-202 b FI(\))p FO(\))426 b(us-)5466 51569 y(mjerni)404
b(grafo)-34 b(vi.)2435 54819 y FL(Niti,)466 b(prostori)f(niti,)h(snop)
39 b(o)-39 b(vi)2435 57123 y FO(Sv)-67 b(aki)311 b(protok)-34
b(ol)312 b(propisuje)h(niz)e(ak)-34 b(cija)312 b(k)-34
b(o)67 b(je)312 b(sv)-67 b(aki)311 b(o)34 b(d)312 b(predvi)p
31307 56510 V(denih)g(sudionik)-67 b(a)312 b(treba)2435
58629 y(izv)-34 b(esti.)1044 b(Pretho)34 b(dni)573 b(se)f(mo)34
b(del)572 b(k)-34 b(oristio)572 b(p)34 b(o)67 b(jmom)574
b FK(r)-62 b(ole)663 b FO(da)573 b(bi)f(ozna)-34 b(\267)-572
b(cio)573 b(ta)67 b(j)573 b(niz,)2435 60134 y(p)34 b(osebno)311
b(de\257nira)67 b(ju)-34 b(\266)-572 b(ci)311 b(rolu)f(inicijatora,)329
b(rolu)310 b(o)34 b(dzivnik)-67 b(a,)327 b(te)310 b(preostale,)329
b(p)34 b(o)310 b(p)34 b(otrebi.)2435 61640 y(U)404 b(o)-34
b(v)g(om)405 b(mo)34 b(delu)404 b(p)34 b(o)67 b(jm)-34
b(u)406 b(role)d(o)34 b(dgo)-34 b(v)-67 b(ara)404 b(p)34
b(o)67 b(jam)405 b(niti.)2435 66029 y FL(De\257nicija)465
b(14)606 b FK(Niti)328 b(su)f(kona)-31 b(\267)-589 b(cni)328
b(nizovi)f(p)-62 b(oruka)326 b(s)i(pr)-62 b(e)g(dznakom,)347
b FG(\276)178 b FO(:)404 b FI(f)p FO(1)p FG(;)202 b(:)g(:)g(:)f(;)h(n)p
FI(g)336 b(!)2435 67535 y(\247)p FG(M)132 b FK(.)4317
70411 y FO(Prik)-67 b(aziv)g(at)434 b(\266)-572 b(cemo)469
b(ih)h(k)-67 b(ao)469 b(grafo)-34 b(v)g(e,)486 b(stoga)471
b(da)67 b(jemo)470 b(alternativn)-34 b(u,)487 b(prikladniju)2435
71916 y(de\257niciju:)21755 74956 y(45)p eop end end
%%Page: 46 46
TeXDict begin HPSdict begin 46 45 bop 7749 7181 a FL(De\257nicija)465
b(15)606 b FO(Nit)309 b FG(\276)353 b FK(je)309 b(usmjer)-62
b(eni)309 b(gr)-62 b(af,)333 b FG(\276)380 b FO(=)336
b(\()p FG(S)s(;)202 b FO(=)-202 b FI(\))p FO(\))p FK(,)335
b(gdje)308 b(je)h FG(S)407 b FO(=)336 b FI(f)p FG(s)42917
7363 y FB(1)43443 7181 y FG(;)202 b(:)g(:)g(:)f(;)h(s)46705
7363 y FF(n)47331 7181 y FI(g)p FK(,)7749 8687 y FG(s)8317
8869 y FF(i)9029 8687 y FO(=)-202 b FI(\))337 b FG(s)11887
8869 y FF(j)12808 8687 y FK(ako)432 b FG(j)406 b FO(=)337
b FG(i)269 b FO(+)g(1)433 b FK(i)h(svaki)d(vrh)i FG(s)26692
8869 y FF(i)27502 8687 y FK(ozna)-31 b(\267)-589 b(cen)432
b(je)h(termom)g(s)h(pr)-62 b(e)g(dznakom.)9631 10945
y FO(Prostor)272 b(niti)h(je)g(skup)g(niti)g(s)g(do)34
b(datnom)274 b(relacijom)e FI(\241)-203 b(!)273 b FO(na)g(vrho)-34
b(vima)273 b({)g(mo)-34 b(\267)-572 b(zemo)7749 12450
y(ga)404 b(promatrati)h(k)-67 b(ao)403 b(bigraf.)7749
14709 y FL(De\257nicija)465 b(16)606 b FO(Prostor)515
b(niti)536 b FK(je)g(bigr)-62 b(af)534 b FO(\(\247)p
FG(;)202 b FO(=)-202 b FI(\))p FG(;)202 b FI(\241)-202
b(!)p FO(\))p FK(,)562 b(gdje)535 b(je)h FO(\247)522
b(=)42409 13800 y Fi(S)43621 14709 y FG(S)44364 14891
y FF(i)45276 14709 y FK(skup)7749 16214 y(vrhova)500
b(niti)i FG(\276)14759 16396 y FF(i)15596 16214 y FO(=)462
b(\()p FG(S)18215 16396 y FF(i)18591 16214 y FG(;)202
b FO(=)-202 b FI(\))21083 16396 y FF(i)21458 16214 y
FO(\))503 b FK(to)-62 b(g)502 b(pr)-62 b(ostor)g(a)500
b(niti,)519 b FO(=)-202 b FI(\))p FO(=)35306 15305 y
Fi(S)36778 16214 y FO(=)g FI(\))38731 16396 y FF(i)39609
16214 y FK(je)502 b(r)-62 b(elacija)500 b(koju)7749 17720
y(smo)365 b(imali)f(prije)g(na)i(nitima,)378 b(a)365
b FI(\241)-202 b(!)366 b FK(p)-62 b(ovezuje)362 b(vrhove)h(r)-62
b(azli)-31 b(\267)-589 b(citih)363 b(niti)i(uz)f(uvjet:)522
b(ako)7749 19225 y FG(s)8317 19422 y FF(ik)9598 19225
y FI(\241)-202 b(!)391 b FG(s)12510 19422 y FF(j)51 b(l)13289
19225 y FK(,)471 b(gdje)463 b(su)g FG(s)18881 19422 y
FF(ik)20162 19225 y FI(2)392 b FG(S)22105 19407 y FF(i)22945
19225 y FK(i)463 b FG(s)24348 19422 y FF(j)51 b(l)25519
19225 y FI(2)391 b FG(S)27461 19407 y FF(j)27949 19225
y FK(,)471 b(onda)463 b(je)g FG(s)33757 19422 y FF(ik)35111
19225 y FK(ozna)-31 b(\267)-589 b(cen)463 b(sa)g FO(+)p
FG(m)h FK(i)g FG(s)45242 19422 y FF(j)51 b(l)46484 19225
y FK(sa)7749 20730 y FI(\241)p FG(m)p FK(.)9631 22989
y FO(Na)485 b(ta)67 b(j)487 b(na)-34 b(\267)-572 b(cin)486
b(je)f(usp)34 b(osta)-34 b(vljena)488 b(k)-34 b(om)g(unik)-67
b(acija)485 b(me)p 35175 22375 364 53 v(du)i(nitima,)506
b FG(k)38 b FO(-ti)486 b(doga)p 46143 22375 V(da)67 b(j)7749
24494 y(na)404 b(niti)g FG(\276)12347 24676 y FF(i)13127
24494 y FO(je)g(slanje)g(p)34 b(oruk)-34 b(e)404 b FG(m)p
FO(,)g(k)-34 b(o)67 b(ja)405 b(je)g(primljena)f(u)g FG(l)24
b FO(-tom)404 b(k)-34 b(oraku)404 b(niti)h FG(\276)44344
24676 y FF(j)44830 24494 y FO(.)7749 26000 y(Za)527 b(protok)-34
b(ole)528 b(predsta)-34 b(vljene)528 b(k)-67 b(ao)527
b(prostore)g(niti,)559 b FI(\241)-203 b(!)528 b FO(zna)-34
b(\267)-572 b(ci)527 b(protok)h(p)34 b(oruk)-34 b(e)527
b(o)34 b(d)7749 27505 y(jednog)553 b(agen)-34 b(ta)553
b(do)f(drugog,)590 b(dok)552 b(=)-202 b FI(\))552 b FO(p)34
b(o)-34 b(v)g(ezuje)553 b(uzastopne)g(p)34 b(oteze)552
b(jednog)h(su-)7749 29011 y(dionik)-67 b(a.)9631 32021
y(Ono)387 b(\267)-542 b(sto)417 b(\267)-572 b(zelimo)450
b(je)h(mo)-34 b(\266)-572 b(ci)450 b(vidjeti)h(k)-67
b(ak)-34 b(o)450 b(se)h(ta)g(k)-34 b(om)g(unik)-67 b(acija)451
b(me)p 41248 31408 V(du)g(agen)-34 b(tima)7749 33527
y(razvijala,)396 b(p)34 b(osebno,)398 b(ona)f(mora)f(bit)g(mogu)-34
b(\266)-572 b(ca)397 b(u)f(vremensk)-34 b(om)396 b(slijedu)g({)g(jo)-64
b(\267)-542 b(s)397 b(uvijek)7749 35032 y(znamo)555 b(samo)h(o)f(nasta)
-34 b(vljanju)558 b(un)-34 b(utar)557 b(jedne)f(niti,)593
b(o)34 b(dnosno)557 b(redoslijedu)e(ak)-34 b(cija)7749
36538 y(un)g(utar)548 b(role.)963 b(No)547 b(protok)-34
b(ol)546 b(je)g(in)-34 b(terak)g(cija)547 b(rola,)580
b(redoslijed)547 b(izvr)-64 b(\267)-542 b(sa)-34 b(v)-67
b(anja)545 b(ak)-34 b(cija)7749 38043 y(role)594 b(jednog)h(agen)-34
b(ta)596 b(o)-34 b(visi)595 b(o)f(drugima.)1111 b(Sljede)-34
b(\266)-572 b(ci)595 b(p)34 b(o)67 b(jam)595 b(go)-34
b(v)g(ori)595 b(o)g(k)-34 b(orektnom)7749 39549 y(slijedu)404
b(ak)-34 b(cija)404 b(u)h(vremen)-34 b(u.)7749 41054
y(Nek)-67 b(a)521 b(su)j(\247)13447 40614 y FB(+)14757
41054 y FO(i)e(\247)16491 40614 y FE(\241)17801 41054
y FO(skup)34 b(o)-34 b(vi)523 b(elemenata)f(iz)g(\247,)552
b(vrho)-34 b(vi)522 b(dek)-34 b(orirani)522 b(p)34 b(ozitivnim)523
b(i)7749 42560 y(negativnim)404 b(p)34 b(oruk)-67 b(ama,)404
b(resp)34 b(ektivno.)7749 44818 y FL(De\257nicija)465
b(17)606 b FO(Snop)319 b FK(je)e(kona)-31 b(\267)-589
b(cni)316 b(pr)-62 b(ostor)316 b(niti)h FO(\(\247)p FG(;)202
b FO(=)-202 b FI(\))p FG(;)202 b FI(\241)-202 b(!)p FO(\))318
b FK(takav)e(da)h(je)g(r)-62 b(elacija)7749 46323 y FI(\241)-203
b(!)460 b FK(bip)-62 b(artitno)g(g)457 b(gr)-62 b(afa)459
b FO(\(\247)20636 45884 y FB(+)21424 46323 y FG(;)202
b FO(\247)22838 45884 y FE(\241)23625 46323 y FG(;)g
FI(\241)-202 b(!)p FO(\))460 b FK(funkcionalna,)k(injektivna,)g(i)c
(surjektivna,)7749 47829 y(a)433 b(r)-62 b(elacija)431
b FO(=)-202 b FI(\))337 b([)f(\241)-202 b(!)434 b FK(acikli)-31
b(\267)-589 b(cka.)9631 50087 y FO(Acikli)-34 b(\267)-572
b(cnost)522 b(osigura)-34 b(v)-67 b(a)522 b(linearno)h(nizanje)g(doga)p
33249 49473 V(da)67 b(ja,)554 b(sv)-34 b(o)67 b(jstv)-67
b(a)524 b FI(\241)-202 b(!)522 b FO(garan)-34 b(ti-)7749
51593 y(ra)67 b(ju)485 b(da)g(je)g(sv)-67 b(ak)g(a)483
b(p)34 b(oruk)-67 b(a)484 b(p)34 b(oslana)485 b(o)34
b(d)485 b(strane)g(jednog)g(p)34 b(o)-64 b(\267)-542
b(siljatelja,)505 b(da)485 b(je)f(sv)-67 b(ak)g(a)7749
53098 y(p)34 b(oruk)-67 b(a)483 b(primljena)h(to)-34
b(\267)-572 b(cno)485 b(jednom.)779 b(F)-101 b(unk)-34
b(cionalnost)486 b(o)34 b(d)484 b FI(\241)-203 b(!)484
b FO(zna)-34 b(\267)-572 b(ci)484 b(da)g(je)g(sv)-67
b(ak)g(a)7749 54603 y(p)34 b(oruk)-67 b(a)326 b(p)34
b(oslana)327 b(samo)g(jednom,)343 b(injektivnost)327
b(zna)-34 b(\267)-572 b(ci)326 b(da)h(je)g(p)34 b(oslana)327
b(p)34 b(oruk)-67 b(a)327 b(priml-)7749 56109 y(jena)284
b(to)-34 b(\267)-572 b(cno)284 b(jednom.)500 b(Surjektivnost)285
b(garan)-34 b(tira)284 b(da)g(je)g(sv)-67 b(ak)g(a)283
b(primljena)h(p)34 b(oruk)-67 b(a)283 b(bila)7749 57614
y(p)34 b(oslana.)627 b(Sv)-34 b(ejedno,)441 b(mogu)434
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b(oruk)-34 b(e)433 b(k)-34 b(o)67 b(je)434 b(nisu)g(primljene.)627
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%%Page: 47 47
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%%Page: 48 48
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%%Page: 49 49
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17718 a FI(\241)p FG(m)4738 b FI(\241)p FG(m)14698 17900
y FB(1)19314 17718 y FI(\241)p FO(\()p FG(m)21792 17900
y FB(1)22318 17718 y FG(;)202 b(m)23921 17900 y FB(2)24447
17718 y FO(\))3342 b FI(\241)p FG(m)4355 b FI(\241f)p
FG(m)p FI(g)37841 17915 y FF(k)6478 18170 y Fi(w)6478
18897 y(w)6478 19624 y(w)6478 20351 y(w)6478 21079 y(\304)13486
18170 y(w)13486 18897 y(w)13486 19624 y(w)13486 20351
y(w)13486 21079 y(\304)21645 18170 y(w)21645 18897 y(w)21645
19624 y(w)21645 20351 y(w)21645 21079 y(\304)28792 18170
y(w)28792 18897 y(w)28792 19624 y(w)28792 20351 y(w)28792
21079 y(\304)36045 18170 y(w)36045 18897 y(w)36045 19624
y(w)36045 20351 y(w)36045 21079 y(\304)5946 22860 y FO(+)p
FG(m)4738 b FI(\241)p FG(m)14698 23042 y FB(2)20850 22860
y FO(+)p FG(m)22857 23042 y FB(1)28457 22860 y FI(\241)p
FG(k)5524 b FI(\241)p FG(k)37167 22420 y FE(0)6478 23311
y Fi(w)6478 24039 y(w)6478 24766 y(w)6478 25493 y(w)6478
26221 y(\304)13486 23311 y(w)13486 24039 y(w)13486 24766
y(w)13486 25493 y(w)13486 26221 y(\304)21645 23311 y(w)21645
24039 y(w)21645 24766 y(w)21645 25493 y(w)21645 26221
y(\304)28792 23311 y(w)28792 24039 y(w)28792 24766 y(w)28792
25493 y(w)28792 26221 y(\304)36045 23311 y(w)36045 24039
y(w)36045 24766 y(w)36045 25493 y(w)36045 26221 y(\304)5946
28002 y FO(+)p FG(m)3202 b FO(+\()p FG(m)13633 28184
y FB(1)14160 28002 y FG(;)202 b(m)15763 28184 y FB(2)16288
28002 y FO(\))4091 b(+)p FG(m)22857 28184 y FB(2)27369
28002 y FO(+)p FI(f)p FG(m)p FI(g)30588 28199 y FF(k)35512
28002 y FO(+)p FG(m)4317 33500 y FO(Ovdje)326 b(p)34
b(osta)67 b(je)327 b(jasan)g(zah)-34 b(tjev)327 b(za)f(funk)-34
b(cionalnosti)327 b(relacije)e FI(\241)-202 b(!)p FO(:)499
b(da)326 b(nije)h(tak)-34 b(o,)2435 35006 y(netk)g(o)339
b(drugi)g(bi)g(mogao)305 b(\267)-572 b(citati)338 b(p)34
b(oruk)-34 b(e)339 b(i)f(me)p 23423 34392 364 53 v(durezultate)h(k)-34
b(o)67 b(je)339 b(uljez)275 b(\267)-542 b(salje)338 b(sam)h(sebi,)2435
36511 y(ali)396 b(to)h(nije)f(to)-34 b(\267)-572 b(cno.)536
b(Nara)-34 b(vno,)398 b(da)f(nije)f(te)g(funk)-34 b(cionalnosti)398
b(ne)e(bi)h(niti)f(bilo)g(p)34 b(otreb)g(e)2435 38016
y(za)404 b(duplik)-67 b(acijsk)-34 b(om)404 b(niti.)2435
39522 y(No,)492 b(sv)-67 b(aku)474 b(p)34 b(oruku)474
b(k)-34 b(o)67 b(ju)476 b(p)34 b(o)-64 b(\267)-542 b(steni)475
b(agen)-34 b(t)475 b(p)34 b(o)-64 b(\267)-542 b(salje)474
b(uljez)g(mo)-34 b(\267)-572 b(ze)474 b(presresti)g(\()p
FK(Flush)93 b FO(\),)2435 41027 y(ili)403 b(je)371 b(\267)-572
b(citati)404 b(i)f(proslijediti)h(\()p FK(Dup)77 b FO(\),)404
b(sebi)g(i)f(ostatku)i(svijeta.)2435 45666 y FH(4.4)1793
b(Analiza)598 b(Dolev-Y)-149 b(ao)597 b(protok)-50 b(ola)2435
48651 y FO(Slijedi)406 b(dok)-67 b(az)404 b(da)i(na)-64
b(\267)-542 b(s)406 b(primjer,)f(Dolev-Y)-101 b(ao)404
b(protok)-34 b(ol)406 b(ja)-34 b(vnog)406 b(klju)-34
b(\267)-572 b(ca,)405 b(ne)h(uspijev)-67 b(a)2435 50156
y(p)34 b(osti)-34 b(\266)-572 b(ci)404 b(ta)67 b(jnost.)2435
51662 y(Uo)-34 b(\267)-572 b(cimo)368 b(da)f(je)h(protok)-34
b(ol)368 b(prekratak)f(da)h(bi)g(nek)-34 b(e)367 b(garancije)g
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y(bile)471 b(zanimljiv)-34 b(e.)741 b(Preciznije,)487
b(nak)-34 b(on)472 b(prv)-34 b(e)472 b(p)34 b(oruk)-34
b(e)471 b(o)34 b(dzivnik)471 b(ne)h(mo)-34 b(\267)-572
b(ze)471 b(biti)h(sigu-)2435 54673 y(ran)455 b(s)f(kim)g(je)g(pri)-34
b(\267)-572 b(cao,)467 b(za)454 b(razliku)f(o)34 b(d)455
b(inicijatora,)466 b(k)-34 b(o)67 b(jem)455 b(mo)-34
b(\267)-572 b(ze)454 b(o)34 b(dgo)-34 b(v)g(oriti)455
b(samo)2435 56178 y(o)34 b(dzivnik)403 b(k)-34 b(o)67
b(jem)405 b(se)f(obra)-34 b(\266)-572 b(ca.)2435 57684
y(Kad)552 b(inicijator)f(dobije)h(p)34 b(o)-34 b(vratn)g(u)552
b(p)34 b(oruku,)588 b(zna)552 b(da)f(je)h(o)34 b(dzivnik)550
b(bio)518 b(\267)-572 b(ziv,)586 b(nitk)-34 b(o)2435
59189 y(drugi)377 b(nije)f(mogao)h(de)-64 b(\267)-542
b(sifrirati)376 b(p)34 b(oruku)376 b(njem)-34 b(u)378
b(namjenjen)-34 b(u.)531 b(Dapa)-34 b(\267)-572 b(ce,)382
b(to)377 b(zna)-34 b(\267)-572 b(ci)375 b(da)2435 60694
y(p)34 b(osjeduje)419 b(inicijatoro)-34 b(vu)418 b(sol,)j(pa)d(se)g
(stoga)g(p)34 b(oklapa)67 b(ju)419 b(u)f(p)34 b(o)g(dacima.)579
b(Mora)67 b(ju)419 b(se)e(i)2435 62200 y(p)34 b(oklapati)405
b(u)f(bro)67 b(ju)405 b(rola,)340 b(\267)-542 b(sto)404
b(je)g(zb)34 b(og)404 b(kratk)-34 b(o)g(\266)-572 b(ce)404
b(protok)-34 b(ola)404 b(o)-34 b(\267)-572 b(cito.)2435
63705 y(Nazo)-34 b(vimo)404 b(sv)-67 b(aki)403 b(vrh)h(ozna)-34
b(\267)-572 b(cen)404 b(p)34 b(ozitivnom)404 b(p)34 b(oruk)-34
b(om)404 b(p)34 b(ozitivnim)403 b(vrhom,)h(a)g(vrh)2435
65211 y(ozna)-34 b(\267)-572 b(cen)404 b(negativnom)h(p)34
b(oruk)-34 b(om)405 b(negativnim)f(vrhom.)2435 70411
y FL(Lema)464 b(4)606 b FK(Pr)-62 b(etp)g(ostavimo)402
b(da)j(je)f FI(B)442 b FK(snop,)410 b FG(t)337 b FI(2)f
FL(M)p FK(,)411 b(i)405 b FG(n)336 b FI(2)h(B)442 b(\271)p
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b FI(f)p FG(s)337 b FI(2)f(B)172 b FO(:)404 b FG(t)336
b FI(v)h FG(ter)34 b(m)p FO(\()p FG(s)p FO(\))p FI(g)p
FK(.)558 b(T)-93 b(ada)433 b FG(t)g FK(izvir)-62 b(e)432
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%%Page: 50 50
TeXDict begin HPSdict begin 50 49 bop 7749 7181 a FK(Dokaz.)528
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FG(s)337 b FI(2)f(B)172 b FO(:)404 b FG(t)336 b FI(v)h
FG(ter)34 b(m)p FO(\()p FG(s)p FO(\))p FI(g)p FO(,)383
b(tada)7749 8687 y(se)422 b(u)h(nijednom)h(vrh)-34 b(u)424
b FG(s)19008 8247 y FE(0)19741 8687 y FO(k)-34 b(o)67
b(ji)423 b(pretho)34 b(di)423 b(vrh)-34 b(u)424 b FG(n)e
FO(u)h(snopu)h FI(B)460 b FO(term)423 b FG(t)f FO(ne)h(p)34
b(o)67 b(ja)-34 b(vljuje)7749 10192 y(k)-67 b(ao)570
b(p)34 b(o)g(dterm.)1038 b(U)570 b(vrh)-34 b(u)571 b
FG(n)f FO(mora)g(biti)h(p)34 b(ozitivna)570 b(p)34 b(oruk)-67
b(a)571 b(jer)f(nema)h(slob)34 b(o)g(dnih)7749 11698
y(negativnih)557 b(vrho)-34 b(v)-67 b(a.)995 b(Za)556
b(sv)-67 b(aki)555 b(negativni)h(vrh)h FG(s)32175 11258
y FE(0)33042 11698 y FO(p)34 b(osto)67 b(ji)557 b(p)34
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13203 y(je)497 b FG(impl)24 b FO(-p)34 b(o)-34 b(v)g(ezan,)520
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b(o)67 b(jem)498 b(bi)f(se)7749 14709 y(p)34 b(o)67 b(ja)-34
b(vljiv)-67 b(ao)404 b(term)g FG(t)p FO(.)538 b FA(\244)7749
17623 y FL(De\257nicija)465 b(19)606 b FK(Pr)-62 b(ostor)412
b(niti)h FO(\(\247)p FG(;)202 b FI(P)100 b FO(\))414
b FK(je)f(D)-31 b(Y)413 b(pr)-62 b(ostor)412 b(ako)g(je)h(unija)f(slje)
-62 b(de)-31 b(\266)-589 b(cih)410 b(niti:)9567 20178
y FI(\262)606 b FK(uljezovih)430 b(niti)j FG(s)337 b
FI(2)g(P)100 b FK(;)9567 22733 y FI(\262)606 b FK(niti)433
b(inicijator)-62 b(a)431 b(danih)i(na)g(slici)f(4.2;)9567
25288 y FI(\262)606 b FK(o)-62 b(dzivnikovih)430 b(niti)j(danih)f(na)i
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b(ostor)g(a.)9631 30744 y FO(U)497 b(analizi)h(Dolev-Y)-101
b(ao)497 b(protok)-34 b(ola)499 b(k)-34 b(o)67 b(ja)498
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b(parametrizirane)e(niti,)j(nego)363 b(\266)-572 b(cemo)396
b(rasu)p 34168 31636 364 53 v(div)-67 b(ati)397 b(o)g(v)-34
b(e)g(\266)-572 b(c)397 b(instanciranim)7749 33755 y(rolama.)730
b(Pritom)435 b(\266)-572 b(cemo)467 b(razmatrati)i(ona)f(izvr)-64
b(\267)-542 b(senja)468 b(rola)g(k)-34 b(o)67 b(ja)435
b(\266)-572 b(ce)468 b(biti)g(mogu)-34 b(\266)-572 b(ca,)485
b(i)7749 35260 y(nama)404 b(zanimljiv)-67 b(a,)403 b(u)i(danom)g
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FO(\))459 b FK(D)-31 b(Y)458 b(pr)-62 b(ostor)456 b(niti.)630
b(T)-93 b(ada)457 b(p)-62 b(ostoji)455 b(snop)j FI(B)495
b FK(s)457 b(uljezovom)7749 39680 y(niti)558 b(koja)g(sadr)-62
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b(gdje)557 b FG(N)32816 39868 y FF(A)34136 39680 y FK(je)-62
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41185 y(inicijator)-62 b(a)431 b FG(I)95 b(nit)p FI(h)p
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41185 y FG(;)g(N)22515 41373 y FF(B)23323 41185 y FI(i)434
b FK(snop)-62 b(a)432 b FI(B)37 b FK(,)434 b(za)f(neke)f
FG(A)i FK(i)g FG(B)61 b FK(,)433 b(i)h FG(K)39466 40675
y FE(\241)p FB(1)39379 41567 y FF(A)41195 41185 y FG(=)-741
b FI(2)337 b FG(P)42983 41367 y FB(0)43509 41185 y FK(.)9631
44086 y FO(Konstruirat)622 b(\266)-572 b(cemo)655 b(tra)-34
b(\267)-572 b(zeni)655 b(snop)i FI(B)692 b FO(k)-34 b(o)67
b(ji)657 b(sadr)-34 b(\267)-572 b(zi)655 b(napad)i(sistematski)e(pre-)
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b(ci)404 b(prostor)h(niti.)7749 47097 y(Pretp)34 b(osta)-34
b(vimo)527 b(da)g(je)492 b(\267)-572 b(cv)-34 b(or)526
b FG(p)h FO(prvi)492 b(\267)-572 b(cv)-34 b(or)526 b(uljezo)-34
b(v)g(e)526 b(niti)h(s)f(p)34 b(oruk)-34 b(om)527 b FG(N)42780
47285 y FF(A)43540 47097 y FO(.)906 b(T)-101 b(o)527
b(je)7749 48602 y(ujedno)496 b(i)f(prvi)f(tak)-67 b(a)-34
b(v)495 b(vrh)g(u)g(snopu,)519 b(s)495 b(obzirom)g(da)g(p)34
b(o)-64 b(\267)-542 b(steni)495 b(sudionik)h(ne)f(bi)g(ob-)7749
50108 y(ja)-34 b(vio)402 b FG(N)11650 50296 y FF(A)12812
50108 y FO(jer)g(su)g(sv)-34 b(e)402 b(p)34 b(oruk)-34
b(e)402 b(protok)-34 b(ola)339 b(\267)-542 b(salju)338
b(\267)-542 b(sifrirane.)537 b(Ispitujemo)403 b(sv)-34
b(e)402 b(mogu)-34 b(\266)-572 b(ce)7749 51613 y(uljezo)-34
b(v)g(e)404 b(niti)g(na)h(k)-34 b(o)67 b(jima)404 b(se)g(mogao)h(p)34
b(o)67 b(ja)-34 b(viti)404 b(vrh)g(sa)h(+)p FG(N)35609
51801 y FF(A)36368 51613 y FO(:)9567 54168 y FI(\262)606
b FK(Init)634 b FO(V)-101 b(rh)520 b(sa)f(+)p FG(N)19332
54356 y FF(A)20611 54168 y FO(ne)h(mo)-34 b(\267)-572
b(ze)518 b(le)-34 b(\267)-572 b(zati)519 b(na)h(o)-34
b(v)g(o)67 b(j)520 b(niti.)884 b(T)-101 b(o)520 b(bi)f(zna)-34
b(\267)-572 b(cilo)519 b(da)g FG(N)46839 54356 y FF(A)10779
55674 y FO(izvire)469 b(na)h(uljezo)-34 b(v)g(o)67 b(j)472
b(niti,)422 b(\267)-542 b(sto)471 b(se)f(k)-34 b(osi)471
b(sa)f(pretp)34 b(osta)-34 b(vk)g(om)472 b(o)e(jedinstv)-34
b(enom)10779 57179 y(izviranju.)9567 59734 y FI(\262)606
b FK(Dup)480 b FO(Ov)-67 b(a)403 b(nas)i(nit)f(ne)g(zanima)g(jer)g(smo)
h(na)-64 b(\267)-542 b(sli)404 b(prvi)f(vrh)h(obilje)-34
b(\267)-572 b(zen)404 b(sa)g(+)p FG(N)46072 59922 y FF(A)46832
59734 y FO(.)9567 62290 y FI(\262)606 b FK(Flush)496
b FO(Nit)404 b(niti)g(nema)g(p)34 b(ozitivnih)404 b(vrho)-34
b(v)-67 b(a.)9567 64845 y FI(\262)606 b FK(Enc)699 b
FO(Kak)-34 b(o)629 b(promatrana)i(sol)f(izvire)e(na)i(inicijatoro)-34
b(v)g(o)67 b(j)631 b(niti,)686 b(i)629 b(radi)h(se)f(o)10779
66350 y(slu)-34 b(\267)-572 b(ca)67 b(jno)g(j)658 b(no)-34
b(v)g(ogenerirano)67 b(j)658 b(vrijednosti,)720 b(nema)657
b(smisla)f(da)h(je)f(inicijator)10715 67856 y(\267)-542
b(sifrira.)9567 70411 y FI(\262)606 b FK(Conc)563 b FO(T)-101
b(ak)-34 b(o)p 16922 69797 V(der,)518 b(ta)496 b(sol)e(nije)h(ni)g
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b(sparena)f(s)10779 71916 y(praznom)405 b(p)34 b(oruk)-34
b(om,)404 b(ali)f(onda)i FG(p)f FO(ne)g(bi)g(bio)h(prvi)e(vrh)h(sa)g(+)
p FG(N)40026 72104 y FF(A)40786 71916 y FO(.)27068 74956
y(50)p eop end end
%%Page: 51 51
TeXDict begin HPSdict begin 51 50 bop 4253 7181 a FI(\262)607
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b(da)h FI(\241)p FO(\()p FG(g)43 b(;)202 b(h)p FO(\))388
b(ozna)-34 b(\267)-572 b(ca)-34 b(v)-67 b(a)5466 8687
y(ulazni)451 b(vrh,)463 b(mo)-34 b(\267)-572 b(zemo)452
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8875 y FF(A)24321 8687 y FO(.)681 b(O)-34 b(\267)-572
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b(je)g(spario)f FG(g)541 b FO(i)497 b FG(h)p FO(,)521
b(on)498 b(je)g(ev)-34 b(en)g(tualno)5466 13203 y(dek)g(omp)34
b(onirao)363 b(dulju)i(k)-34 b(onk)-67 b(atenaciju,)371
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b(cujemo)342 b(da)h(je)5466 17720 y(k)-34 b(onk)-67 b(atenaciju)379
b(morao)g(primiti)314 b(\267)-542 b(sifriran)-34 b(u,)384
b(jer)379 b(sparene)f(p)34 b(oruk)-34 b(e)379 b(ne)g(izviru)e(na)5466
19225 y(regularnim)362 b(nitima.)525 b(T)-101 b(ada)364
b(je)g(ona)f(morala)g(biti)299 b(\267)-542 b(sifrirana)363
b(uljezo)-34 b(vim)363 b(ja)-34 b(vnim)5466 20730 y(klju)g(\267)-572
b(cem,)466 b(jer)453 b(niti)h(jedn)-34 b(u)456 b(drugu)f(enkrip)34
b(ciju)454 b(ne)g(bi)g(mogao)g(otv)-34 b(oriti.)688 b(T)-101
b(akv)-67 b(a)5402 22236 y(\267)-542 b(sifrirana)452
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b(ao)451 b(p)34 b(o)g(dterm,)464 b(na)453 b(niti)f(p)34
b(o)-64 b(\267)-542 b(stenog)453 b(agen)-34 b(ta.)5466
23741 y(Razmotrimo)404 b(dv)-67 b(a)404 b(mogu)-34 b(\266)-572
b(ca)404 b(slu)-34 b(\267)-572 b(ca)67 b(ja:)6583 26456
y(1.)606 b(Radi)546 b(se)g(o)g(p)34 b(oruci)545 b(oblik)-67
b(a)545 b FI(f)p FG(m)23130 26638 y FB(1)23656 26456
y FG(;)202 b(N)25169 26644 y FF(A)25929 26456 y FG(;)g(m)27532
26638 y FB(2)28058 26456 y FI(g)28664 26644 y FF(K)29457
26793 y FC(E)30747 26456 y FO(k)-34 b(o)67 b(ja)546 b(je)g(p)34
b(o)g(dterm)546 b(v)-34 b(e)g(\266)-572 b(ce)8132 27962
y(p)34 b(oruk)-34 b(e)526 b(k)-34 b(o)67 b(ja)527 b(izvire)e(na)h(o)34
b(dzivnik)-34 b(o)g(v)g(o)67 b(j)527 b(niti.)904 b(Sol)526
b FG(N)33611 28150 y FF(A)34897 27962 y FO(izvire)f(u)h(prv)-34
b(o)67 b(j)8132 29467 y(p)34 b(oruci)501 b(inicijatora)f
FG(A)h FO(k)-34 b(o)67 b(ji)468 b(\267)-572 b(zeli)499
b(pri)-34 b(\267)-572 b(cati)500 b(s)h FG(B)61 b FO(-om)501
b(te)g(je)g FG(A)g FO(sigurno)g(ne)8068 30973 y(\267)-542
b(salje)452 b(na)g(o)-34 b(v)-67 b(a)67 b(j)452 b(na)-34
b(\267)-572 b(cin.)682 b(No,)464 b(niti)452 b(o)34 b(dzivnik)450
b(ne)388 b(\267)-542 b(salje)452 b(ne)-64 b(\267)-542
b(sto)452 b(o)-34 b(v)g(og)453 b(oblik)-67 b(a)8132 32478
y(k)g(ao)319 b(o)34 b(dgo)-34 b(v)g(or)319 b(na)h FG(A)p
FO(-o)-34 b(vu)320 b(p)34 b(oruku.)510 b(T)-101 b(ak)-34
b(o)p 27325 31865 364 53 v(der,)337 b(niti)319 b(k)-67
b(ao)318 b(o)34 b(dgo)-34 b(v)g(or)320 b(na)g(neku)8132
33984 y FG(E)70 b FO(-o)-34 b(vu)280 b(p)34 b(oruku)279
b({)h(tada)g(bi)f FG(E)349 b FO(v)-34 b(e)g(\266)-572
b(c)278 b(bio)i(znao)f(sol.)497 b(Ono)215 b(\267)-542
b(sto)280 b(je)f(uljez)h(mogao)8132 35489 y(imati)529
b(\()-64 b(\267)-542 b(sto)529 b(mo)-34 b(\267)-572 b(zemo)528
b(gledati)h(k)-67 b(ao)528 b(sp)34 b(ecijalan)528 b(slu)-34
b(\267)-572 b(ca)67 b(j)529 b(gornje)g(p)34 b(oruk)-34
b(e,)8132 36995 y(gdje)415 b(su)f FG(m)13364 37177 y
FB(1)14305 36995 y FO(i)f FG(m)16119 37177 y FB(2)17059
36995 y FO(prazne\))i(je)f FI(f)p FG(N)24353 37183 y
FF(A)25113 36995 y FI(g)25719 37183 y FF(K)26512 37332
y FC(E)27256 36995 y FO(.)569 b(O)414 b(tome)g(pak)g(diskutiramo)g(u)
8132 38500 y(slu)-34 b(\267)-572 b(ca)67 b(ju)405 b FK(De)-62
b(c)p FO(.)6583 40555 y(2.)606 b(Ak)-34 b(o)616 b(se)g(radilo)g(o)g(p)
34 b(oruci)615 b FI(ff)p FG(m)23602 40737 y FB(1)24128
40555 y FI(g)24734 40743 y FF(K)25527 40892 y FC(E)26272
40555 y FG(;)202 b(N)27785 40743 y FF(A)28544 40555 y
FI(g)29150 40743 y FF(K)29943 40892 y FC(E)31304 40555
y FO(morao)615 b(ju)i(je)f(kreirati)8132 42060 y(o)34
b(dzivnik.)538 b(No)404 b(on)h(sigurno)f(ne)g(bi)g(p)34
b(obrk)-67 b(ao)404 b(sol)g(i)g(vlastito)g(ime.)4253
44775 y FI(\262)607 b FK(De)-62 b(c)540 b FO(Preosta)67
b(je)473 b(slu)-34 b(\267)-572 b(ca)67 b(j)473 b(k)-67
b(ada)472 b(uljez)g(dobiv)-67 b(a)473 b(sol)408 b(\267)-542
b(sifriran)-34 b(u)473 b(vlastitim)f(ja)-34 b(vnim)5466
46281 y(klju)g(\267)-572 b(cem,)558 b FI(f)p FG(N)12049
46469 y FF(A)12809 46281 y FI(g)13415 46469 y FF(K)14208
46618 y FC(E)14952 46281 y FO(.)911 b(Dalje)494 b(\266)-572
b(cemo)527 b(istra)-34 b(\267)-572 b(ziti)527 b(tu)i(mogu)-34
b(\266)-572 b(cnost)529 b(i)f(p)34 b(ok)-67 b(azati)527
b(da)5466 47786 y(v)-34 b(o)34 b(di)404 b(na)g(napad.)2435
50940 y FL(Lema)464 b(6)606 b FK(A)-31 b(ko)474 b(p)-62
b(ostoji)471 b(uljezova)g(nit)j(obilje)-62 b(\267)-558
b(zena)472 b(sa)h FI(\241f)p FG(N)30268 51128 y FF(A)31028
50940 y FI(g)31634 51128 y FF(K)32427 51277 y FC(E)33171
50940 y FK(,)484 b(tada)473 b(p)-62 b(ostoji)471 b(o)-62
b(d-)2435 52445 y(zivnikova)431 b(nit)j(sa)f(p)-62 b(orukom)431
b FI(ff)p FG(N)18266 52633 y FF(A)19026 52445 y FI(g)19632
52633 y FF(K)20425 52782 y FC(E)21170 52445 y FG(;)202
b(x)p FI(g)23008 52633 y FF(K)23801 52782 y FC(E)24545
52445 y FK(.)2435 55546 y(Dokaz.)634 b FO(T)-101 b(erm)436
b FI(f)p FG(N)11464 55734 y FF(A)12224 55546 y FI(g)12830
55734 y FF(K)13623 55883 y FC(E)14804 55546 y FO(je)g(p)34
b(o)g(dterm)437 b(p)34 b(oruk)-34 b(e)436 b(k)-34 b(o)67
b(ju)438 b(o)34 b(dzivnik)435 b(sta)-34 b(vlja)437 b(na)g(mre)-34
b(\267)-572 b(zu{)2435 57051 y(nara)-34 b(vno,)424 b(da)c(se)g(radilo)f
(o)h(inicijatoru,)j(to)d(bi)g(bila)f(regularna)g(runda)i(izme)p
38154 56437 V(du)f(inici-)2435 58557 y(jatora)375 b(Alice)e(i)g(zle)g
(Ev)-34 b(e.)529 b(No)374 b(to)g(nije)g(mogu)-34 b(\266)-572
b(ce,)380 b(jer)374 b(sol)f(jedinstv)-34 b(eno)376 b(izvire)c(na)i
(niti)g(u)2435 60062 y(k)-34 b(o)67 b(jo)g(j)406 b(Alice)d(na)-34
b(\267)-572 b(cinje)404 b(rundu)i(s)e(Bob)34 b(om.)2435
61567 y(Ak)-34 b(o)270 b(neki)f FG(x)g FO(o)34 b(dgo)-34
b(v)-67 b(ara)269 b(Evi,)295 b(o)34 b(dgo)-34 b(v)g(or)270
b(je)g(oblik)-67 b(a)268 b FI(ff)p FG(N)26913 61755 y
FF(A)27674 61567 y FI(g)28280 61755 y FF(K)29073 61904
y FC(E)29817 61567 y FG(;)202 b(x)p FI(g)31655 61755
y FF(K)32448 61904 y FC(E)33192 61567 y FO(,)296 b(nak)-34
b(on)270 b(pretho)34 b(dno)2435 63073 y(dobiv)-34 b(enog)405
b FI(ff)p FG(N)10345 63261 y FF(A)11105 63073 y FI(g)11711
63270 y FF(k)12201 63381 y FC(x)12776 63073 y FG(;)202
b(E)70 b FI(g)14886 63270 y FF(k)15376 63381 y FC(x)16353
63073 y FO(o)34 b(d)404 b(Ev)-34 b(e.)539 b FA(\244)2435
66137 y FO(Ozna)-34 b(\267)-572 b(cimo)404 b(sa)g FG(\262)g
FO(prazn)-34 b(u)405 b(p)34 b(oruku.)2435 68905 y FL(Lema)464
b(7)606 b FK(A)-31 b(ko)358 b(p)-62 b(ostoji)355 b(uljezova)g(nit)j(s)g
(vrhom)f(obilje)-62 b(\267)-558 b(zenim)355 b(sa)j FI(\241ff)p
FG(N)55 b(A)p FI(g)37002 69093 y FF(K)37795 69242 y FC(E)38539
68905 y FG(;)202 b(x)p FI(g)40377 69093 y FF(K)41170
69242 y FC(E)41914 68905 y FK(,)2435 70411 y(tada)387
b(p)-62 b(ostoji)386 b(o)-62 b(dzivnikova)384 b(nit)k(s)g(p)-62
b(orukom)387 b FI(f)p FG(m)24603 70593 y FB(1)25129 70411
y FG(;)202 b FI(ff)p FG(N)27854 70599 y FF(A)28614 70411
y FI(g)29220 70608 y FF(k)29710 70719 y FC(x)30284 70411
y FG(;)g(m)31887 70593 y FB(2)32413 70411 y FI(g)33019
70599 y FF(K)33812 70748 y FC(E)34556 70411 y FG(;)g(y)43
b FI(g)36338 70599 y FF(K)37131 70748 y FC(E)37876 70411
y FK(,)397 b(gdje)387 b(su)2435 71916 y FG(m)3499 72098
y FB(1)4025 71916 y FK(,)434 b FG(m)5895 72098 y FB(2)6855
71916 y FI(2)336 b(\247)p FO(\()p FL(M)270 b FI([)f(f)p
FG(\262)p FI(g)p FO(\))p FK(.)21755 74956 y FO(51)p eop
end end
%%Page: 52 52
TeXDict begin HPSdict begin 52 51 bop 7749 7181 a FK(Dokaz.)533
b FO(Ev)-67 b(a)391 b(je)i(morala)f(nek)-67 b(ak)-34
b(o)392 b(proizv)-34 b(esti)392 b FI(ff)p FG(N)31226
7369 y FF(A)31986 7181 y FI(g)32592 7378 y FF(k)33082
7489 y FC(x)33656 7181 y FG(;)202 b(E)70 b FI(g)35766
7378 y FF(k)36256 7489 y FC(x)36830 7181 y FO(.)535 b(Nije)392
b(ju)h(uh)-34 b(v)-67 b(atila)393 b(na)7749 8687 y(mre)-34
b(\267)-572 b(zi)397 b(jer)h(se)f(nijedan)i(p)34 b(o)-64
b(\267)-542 b(steni)399 b(sudionik)f(ne)g(bi)g(predsta)-34
b(vljao)400 b(u)e(njeno)h(ime.)536 b(Dalje,)7749 10192
y(Ev)-67 b(a)454 b(nije)g(kreirala)f(cijelu)i(p)34 b(oruku.)690
b(Preciznije,)466 b(nije)454 b(mogla)h(kreirati)e FI(f)p
FG(N)42981 10380 y FF(A)43741 10192 y FI(g)44347 10389
y FF(k)44837 10500 y FC(x)45412 10192 y FO(,)466 b(jer)7749
11698 y(bi)404 b(to)g(zna)-34 b(\267)-572 b(cilo)404
b(p)34 b(ozna)-34 b(v)-67 b(anje)404 b FG(N)21921 11886
y FF(A)23085 11698 y FO(k)-34 b(o)67 b(ja)405 b(jedinstv)-34
b(eno)406 b(izvire)c(na)j(inicijatoro)-34 b(v)g(o)67
b(j)405 b(niti)f(.)9631 14709 y(Dakle,)705 b(enkrip)34
b(cija)646 b FI(f)p FG(N)21170 14897 y FF(A)21930 14709
y FI(g)22536 14906 y FF(k)23026 15017 y FC(x)24247 14709
y FO(je)g(p)34 b(o)g(dterm)646 b(nek)-34 b(e)647 b(p)34
b(oruk)-34 b(e)646 b(o)34 b(dzivnik)-67 b(a.)1264 b(Kak)-34
b(o)7749 16214 y(p)34 b(oruk)-67 b(a)458 b FI(ff)p FG(N)14033
16402 y FF(A)14793 16214 y FI(g)15399 16411 y FF(k)15889
16522 y FC(x)16463 16214 y FG(;)202 b(E)70 b FI(g)18573
16411 y FF(k)19063 16522 y FC(x)20095 16214 y FO(nije)458
b(bila)g(cijeli)g(o)34 b(dgo)-34 b(v)g(or,)472 b(preosta)67
b(je)459 b(samo:)647 b(o)34 b(dzivnik)457 b(je)7749 17720
y(p)34 b(obrk)-67 b(ao)404 b FI(f)p FG(N)13979 17908
y FF(A)14739 17720 y FI(g)15345 17917 y FF(k)15835 18028
y FC(x)16813 17720 y FO(za)g(sol,)f(ili)h(dio)g(soli.)9567
20012 y FI(\262)606 b FO(Ak)-34 b(o)293 b(je)f(p)34 b(oruk)-67
b(a)292 b FI(ff)p FG(N)20512 20200 y FF(A)21272 20012
y FI(g)21878 20209 y FF(k)22368 20320 y FC(x)22943 20012
y FG(;)202 b(E)70 b FI(g)25053 20209 y FF(k)25543 20320
y FC(x)26409 20012 y FO(bila)292 b(dio)g(o)34 b(dgo)-34
b(v)g(ora,)315 b(morala)292 b(je)h(biti)228 b(\267)-542
b(sifrirana)10779 21517 y(Evinim)485 b(ja)-34 b(vnim)486
b(klju)-34 b(\267)-572 b(cem)486 b(da)g(bi)f(je)h(Ev)-67
b(a)485 b(mogla)h(de)-64 b(\267)-542 b(sifrirati.)782
b(Kao)486 b(o)34 b(dgo)-34 b(v)g(or)10779 23023 y(p)34
b(o)-64 b(\267)-542 b(stenog)425 b(agen)-34 b(ta)425
b(bila)f(je)g(smje)-64 b(\267)-542 b(stena)425 b(u)f
FI(ffff)p FG(N)33576 23211 y FF(A)34337 23023 y FI(g)34943
23220 y FF(k)35433 23331 y FC(x)36007 23023 y FG(;)202
b(E)70 b FI(g)38117 23220 y FF(k)38607 23331 y FC(x)39181
23023 y FI(g)39787 23211 y FF(K)40580 23360 y FC(E)41324
23023 y FG(;)202 b(y)43 b FI(g)43106 23211 y FF(K)43899
23360 y FC(E)44644 23023 y FO(.)598 b(Od-)10779 24528
y(zivnik)515 b(je)g(pretho)34 b(dno)517 b(o)34 b(d)516
b(Ev)-34 b(e)515 b(dobio)i FI(ffff)p FG(N)32948 24716
y FF(A)33708 24528 y FI(g)34314 24725 y FF(k)34804 24836
y FC(x)35378 24528 y FG(;)202 b(E)70 b FI(g)37488 24725
y FF(k)37978 24836 y FC(y)38532 24528 y FI(g)39138 24716
y FF(K)39931 24865 y FC(E)40676 24528 y FG(;)202 b(E)70
b FI(g)42786 24725 y FF(k)43276 24836 y FC(y)43830 24528
y FO(.)873 b(Ov)-67 b(a)67 b(j)10779 26034 y(p)34 b(oku)-64
b(\267)-542 b(sa)67 b(j)405 b(nije)f(tra)-34 b(\267)-572
b(zeni,)404 b(Evi)f(p)34 b(ono)-34 b(vno)405 b(fali)f(ista)h
(informacija.)9567 28452 y FI(\262)606 b FO(Odzivnik)263
b(\267)-542 b(salje)328 b FI(f)p FG(N)20126 28640 y FF(A)20886
28452 y FI(g)21492 28649 y FF(k)21982 28760 y FC(x)22884
28452 y FO(u)g FI(fff)p FG(N)26677 28640 y FF(A)27438
28452 y FI(g)28044 28649 y FF(k)28534 28760 y FC(x)29108
28452 y FI(g)29714 28640 y FF(K)30507 28789 y FC(E)31251
28452 y FG(;)202 b(y)43 b FI(g)33033 28640 y FF(K)33826
28789 y FC(E)34571 28452 y FO(,)279 b(\267)-542 b(sto)328
b(je)g(o)34 b(dgo)-34 b(v)g(or)328 b(na)h(Evin)-34 b(u)10779
29957 y FI(fff)p FG(N)13571 30145 y FF(A)14331 29957
y FI(g)14937 30154 y FF(k)15427 30265 y FC(x)16001 29957
y FI(g)16607 30154 y FF(k)17097 30265 y FC(y)17652 29957
y FG(;)202 b(E)70 b FI(g)19762 30154 y FF(k)20252 30265
y FC(y)20807 29957 y FO(.)610 b(Op)34 b(et)428 b(ne)h(idemo)f(u)g
(dobrom)h(smjeru,)434 b(vra)-34 b(\266)-572 b(camo)428
b(se)g(na)10779 31463 y(mjesto)405 b(gdje)f(Evi)g(nedosta)67
b(je)405 b FI(f)p FG(N)26463 31651 y FF(A)27224 31463
y FI(g)27830 31660 y FF(k)28320 31771 y FC(x)28894 31463
y FO(.)9567 33880 y FI(\262)606 b FO(P)-34 b(opra)g(vlja)67
b(ju)-34 b(\266)-572 b(ci)380 b(p)34 b(osljednji)379
b(slu)-34 b(\267)-572 b(ca)67 b(j,)383 b(vidimo)378 b(da)h(smo)g(uz)f
FI(f)p FG(N)38756 34068 y FF(A)39516 33880 y FI(g)40122
34077 y FF(k)40612 34188 y FC(x)41564 33880 y FO(mogli)g(imati)10779
35386 y(ne)-64 b(\267)-542 b(sto)569 b(spareno,)610 b(prije)568
b(no)505 b(\267)-542 b(sto)568 b(se)h(sv)-34 b(e)504
b(\267)-542 b(sifrirano)568 b(sa)g FG(K)37428 35574 y
FF(E)38223 35386 y FO(.)1032 b(U)568 b(op)-34 b(\266)-572
b(cem)568 b(bi)g(se)10779 36891 y(slu)-34 b(\267)-572
b(ca)67 b(ju)363 b(radilo)e(o)g(p)34 b(oruci)361 b(oblik)-67
b(a)361 b FI(ff)p FG(m)28714 37073 y FB(1)29240 36891
y FG(;)202 b FI(f)p FG(N)31359 37079 y FF(A)32119 36891
y FI(g)32725 37088 y FF(k)33215 37199 y FC(x)33789 36891
y FG(;)g(m)35392 37073 y FB(2)35918 36891 y FI(g)36524
37079 y FF(K)37317 37228 y FC(E)38061 36891 y FG(;)g(y)43
b FI(g)39843 37079 y FF(K)40636 37228 y FC(E)41381 36891
y FO(,)370 b(gdje)362 b FG(m)45702 37073 y FB(1)46589
36891 y FO(ili)10779 38397 y FG(m)11843 38579 y FB(2)12773
38397 y FO(ne)404 b(mora)g(biti)h(prisutna.)7749 40689
y FA(\244)9631 43700 y FO(Ev)-67 b(a)637 b(je)h(morala)f(o)34
b(daslati)638 b FI(f)p FG(m)24552 43882 y FB(1)25079
43700 y FG(;)202 b FI(ff)p FG(N)27804 43888 y FF(A)28563
43700 y FI(g)29169 43897 y FF(k)29659 44008 y FC(x)30234
43700 y FG(;)g(m)31837 43882 y FB(2)32362 43700 y FI(g)32968
43897 y FF(k)33458 44008 y FC(y)34013 43700 y FG(;)g(E)70
b FI(g)36123 43897 y FF(k)36613 44008 y FC(y)37168 43700
y FO(,)696 b(za)573 b(\267)-542 b(sto)639 b(jo)67 b(j)639
b(trebao)7749 45205 y FI(f)p FG(N)9329 45393 y FF(A)10089
45205 y FI(g)10695 45402 y FF(k)11185 45513 y FC(x)12163
45205 y FO(otprije.)7749 46711 y(Mogla)502 b(je)h(imati)f
FI(f)p FG(m)17862 46893 y FB(1)18388 46711 y FG(;)202
b FI(f)p FG(N)20507 46899 y FF(A)21267 46711 y FI(g)21873
46908 y FF(k)22363 47019 y FC(x)22937 46711 y FG(;)g(m)24540
46893 y FB(2)25066 46711 y FI(g)25672 46908 y FF(k)26162
47019 y FC(y)26717 46711 y FO(,)527 b(i)502 b(to)h(je)g(klju)-34
b(\267)-572 b(c)502 b(za)g(napad:)737 b(radi)503 b(se)f(o)g(bilo)7749
48216 y(k)-34 b(o)67 b(jo)g(j)357 b(o)34 b(d)355 b(p)34
b(oruk)-67 b(a)355 b(Alice)f(ili)h(Boba)g(iz)g(prv)-34
b(e,)365 b(regularne)355 b(runde.)523 b(U)355 b(oba)h(slu)-34
b(\267)-572 b(ca)67 b(ja,)365 b FG(y)399 b FO(i)356 b
FG(x)7749 49722 y FO(se)329 b(p)34 b(o)g(dudara)67 b(ju,)346
b FG(m)17005 49904 y FB(1)17860 49722 y FO(ne)329 b(p)34
b(osto)67 b(ji,)345 b(a)330 b FG(m)25725 49904 y FB(2)26580
49722 y FO(je)f(ime)g(Evinog)g(sugo)-34 b(v)g(ornik)-67
b(a.)514 b(Ak)-34 b(o)330 b(o)34 b(dab)g(er-)7749 51227
y(emo)316 b(da)h(je)f FG(x)g FO(Bob,)334 b(a)316 b FG(m)18845
51409 y FB(2)19687 51227 y FO(Alicino)g(name,)334 b(dok)-67
b(azali)315 b(smo)i(lem)-34 b(u)316 b(5,)334 b(a)316
b(skica)g(napada)h(je:)10184 54799 y FG(A)12374 53874
y FI(ff)p FG(N)14560 54062 y FF(A)15320 53874 y FI(g)15926
54071 y FF(k)16416 54220 y FC(B)17174 53874 y FG(;)202
b(A)p FI(g)19228 54071 y FF(k)19718 54220 y FC(B)12200
54799 y FI(\241)-277 b(\241)-269 b(\241)f(\241)h(\241)f(\241)g(\241)h
(\241)f(\241)h(\241)f(\241)-276 b(!)1107 b FG(B)10184
57207 y(A)12528 56281 y FI(ff)p FG(N)14714 56469 y FF(A)15475
56281 y FI(g)16081 56478 y FF(k)16571 56627 y FC(A)17295
56281 y FG(;)202 b(B)61 b FI(g)19420 56478 y FF(k)19910
56627 y FC(A)12200 57207 y FI(\303)-277 b(\241)-269 b(\241)f(\241)h
(\241)f(\241)h(\241)f(\241)h(\241)f(\241)g(\241)-276
b(\241)1107 b FG(B)21921 59615 y(E)23767 58689 y FI(fff)p
FG(N)26559 58877 y FF(A)27319 58689 y FI(g)27925 58886
y FF(k)28415 59035 y FC(B)29173 58689 y FG(;)202 b(A)p
FI(g)31227 58886 y FF(k)31717 59035 y FC(B)32475 58689
y FG(;)g(E)70 b FI(g)34585 58886 y FF(k)35075 59035 y
FC(B)24000 59615 y FI(\241)-385 b(\241)-270 b(\241)g(\241)h(\241)f
(\241)h(\241)f(\241)g(\241)h(\241)f(\241)h(\241)f(\241)g(\241)h(\241)f
(\241)-385 b(!)1107 b FG(B)21921 62022 y(E)23930 61097
y FI(fff)p FG(N)26722 61285 y FF(A)27482 61097 y FI(g)28088
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y FF(])34705 63723 y FB(1)15670 65474 y FO(=)-202 b FI(\))17623
65656 y FB(2)18486 65474 y FO(=)269 b(=)-202 b FI(\))21651
65656 y FB(1)29867 65474 y FO(=)g FI(\))31820 64885 y
FF(])31820 65822 y FB(2)32683 65474 y FO(=)269 b(=)-202
b FI(\))35848 64885 y FF(])35848 65822 y FB(1)15670 67574
y FI(\241)g(!)17623 67756 y FB(2)18486 67574 y FO(=)269
b FI(\241)-202 b(!)21651 67756 y FB(1)29867 67574 y FI(\241)g(!)31820
66984 y FF(])31820 67921 y FB(2)32683 67574 y FO(=)269
b FI(\241)-202 b(!)35848 66984 y FF(])35848 67921 y FB(1)36710
67574 y FI([)270 b(f)p FO(\()p FG(v)39453 67756 y FB(1)39978
67574 y FG(;)202 b(v)41105 67756 y FB(2)41630 67574 y
FO(\))p FI(g)10779 70411 y FO(U)549 b(no)-34 b(v)g(o)67
b(j)551 b(k)-34 b(on\257guraciji)550 b(do)34 b(dat)550
b(je)f(jedan)h FI(\241)-202 b(!)549 b FO(brid,)585 b(k)-34
b(o)67 b(ji)550 b(ozna)-34 b(\267)-572 b(ca)-34 b(v)-67
b(a)549 b(slanje)10779 71916 y(p)34 b(oruk)-34 b(e)404
b FG(m)g FO(iz)g(vrha)g FG(v)20923 72098 y FB(1)21852
71916 y FO(k)-67 b(a)404 b(vrh)-34 b(u)404 b FG(v)26854
72098 y FB(2)27380 71916 y FO(.)27068 74956 y(56)p eop
end end
%%Page: 57 57
TeXDict begin HPSdict begin 57 56 bop 4253 7181 a FI(\262)607
b FO(Slanje)404 b(p)34 b(oruk)-34 b(e)5466 8687 y(Situacija)431
b(se)g(razlikuje)f(o)34 b(d)431 b(pretho)34 b(dne)432
b(u)g(tome)367 b(\267)-542 b(sto)431 b(je)g(vrh)g FG(v)34730
8869 y FB(1)35687 8687 y FO(=)-202 b FI(\))p FO(-p)34
b(o)-34 b(v)g(ezan)5466 10192 y(s)487 b(vrhom)g FG(v)530
b FO(iste)487 b(niti.)788 b(V)-101 b(rho)-34 b(vi)488
b FG(v)21276 10374 y FB(1)22276 10192 y FO(=)475 b(+)p
FG(m)488 b FO(i)e FG(v)27600 10374 y FB(2)28601 10192
y FO(=)475 b FI(\241)p FG(m)487 b FO(pripada)67 b(ju)489
b FG(S)38968 9603 y FF(])38898 10539 y FB(1)39749 10192
y FI(n)325 b FG(S)41423 10374 y FB(1)41949 10192 y FO(,)5466
11855 y(p)34 b(osto)67 b(ji)415 b FG(v)396 b FI(2)354
b FG(S)484 b FO(tak)-67 b(a)-34 b(v)414 b(da)h FG(v)396
b FO(=)-202 b FI(\))20803 11265 y FF(])20803 12202 y
FB(1)21683 11855 y FG(v)22271 12037 y FB(1)22796 11855
y FO(,)416 b(no)f(nema)f(=)-202 b FI(\))30438 11415 y
FF(])30859 11855 y FO(-brida)415 b(k)-34 b(o)67 b(ji)415
b(ulazi)e(u)i FG(v)41424 12037 y FB(2)41949 11855 y FO(.)5466
13360 y(Slanje)404 b(p)34 b(oruk)-34 b(e)404 b(prema)g
FG(m)h FO(prema)f FG(v)22549 13542 y FB(2)23478 13360
y FO(da)67 b(je:)10549 16061 y FG(S)11292 16243 y FB(2)12155
16061 y FO(=)336 b FG(S)14177 16243 y FB(1)14973 16061
y FI([)538 b(f)p FG(v)17513 16243 y FB(1)18039 16061
y FI(g)8136 b FG(S)27594 15471 y FF(])27524 16408 y FB(2)28387
16061 y FO(=)336 b FG(S)30479 15471 y FF(])30409 16408
y FB(1)9339 18160 y FO(=)-202 b FI(\))11292 18342 y FB(2)12155
18160 y FO(=)269 b(=)-202 b FI(\))15320 18342 y FB(1)16182
18160 y FI([)270 b(f)p FO(\()p FG(v)43 b(;)202 b(v)20095
18342 y FB(1)20620 18160 y FO(\))p FI(g)3874 b FO(=)-202
b FI(\))27524 17570 y FF(])27524 18507 y FB(2)28387 18160
y FO(=)269 b(=)-202 b FI(\))31552 17570 y FF(])31552
18507 y FB(1)9339 20259 y FI(\241)g(!)11292 20441 y FB(2)12155
20259 y FO(=)269 b FI(\241)-202 b(!)15320 20441 y FB(1)25571
20259 y FI(\241)g(!)27524 19669 y FF(])27524 20606 y
FB(2)28387 20259 y FO(=)269 b FI(\241)-202 b(!)31552
19669 y FF(])31552 20606 y FB(1)32414 20259 y FI([)270
b(f)p FO(\()p FG(v)35157 20441 y FB(1)35683 20259 y FG(;)202
b(v)36810 20441 y FB(2)37335 20259 y FO(\))p FI(g)5466
22960 y FO(Ov)-67 b(a)67 b(j)368 b(put)j(smo)e(se)f(p)34
b(obrin)-34 b(uli)370 b(da)f(no)-34 b(v)-67 b(a)369 b(k)-34
b(on\257guracija)370 b(sadr)-34 b(\267)-572 b(zi)369
b(informaciju)g(da)5466 24465 y FG(v)6054 24647 y FB(1)6983
24465 y FO(ima)404 b(=)-202 b FI(\))p FO(-pretho)34 b(dnik)-67
b(a)404 b FG(v)43 b FO(.)4253 26959 y FI(\262)607 b FO(P)-34
b(o)g(\267)-572 b(cetno)404 b(primanje)h(p)34 b(oruk)-34
b(e)5466 28465 y(Sli)g(\267)-572 b(cno)457 b(p)34 b(o)-34
b(\267)-572 b(cetnom)458 b(slanju)g(p)34 b(oruk)-34 b(e:)645
b(imamo)458 b(vrho)-34 b(v)g(e)457 b FG(v)31457 28647
y FB(1)32408 28465 y FO(=)425 b(+)p FG(m)458 b FO(i)f
FG(v)37623 28647 y FB(2)38574 28465 y FO(=)425 b FI(\241)p
FG(m)p FO(,)5466 29970 y(no)325 b(sada)h FG(v)10347 30152
y FB(1)11209 29970 y FI(2)337 b FG(S)13097 30152 y FB(1)13948
29970 y FO({)326 b(p)34 b(oruk)-67 b(a)325 b FG(m)g FO(je)h(p)34
b(oslana,)341 b FG(v)26748 30152 y FB(2)27598 29970 y
FO(pripada)326 b FG(S)32780 29380 y FF(])32710 30317
y FB(1)33348 29970 y FI(n)112 b FG(S)34809 30152 y FB(1)35335
29970 y FO(,)341 b(i)325 b FG(v)37263 30152 y FB(1)38125
29970 y FI(\241)-202 b(!)40078 29530 y FF(])40836 29970
y FG(v)41424 30152 y FB(2)41949 29970 y FO(.)5466 31476
y(Nema)404 b(ulaznog)g(=)-202 b FI(\))p FO(-brida)404
b(k)-34 b(o)34 b(d)405 b FG(v)21815 31658 y FB(2)22340
31476 y FO(.)23283 31169 y(\267)23215 31476 y(Zelimo)e(da)i
FG(v)29460 31658 y FB(2)30389 31476 y FO(primi)f(p)34
b(oruku)404 b FG(m)p FO(:)12500 34176 y FG(S)13243 34358
y FB(2)14105 34176 y FO(=)337 b FG(S)16128 34358 y FB(1)16923
34176 y FI([)539 b(f)p FG(v)19464 34358 y FB(2)19990
34176 y FI(g)10569 b FG(S)31978 33587 y FF(])31908 34523
y FB(2)32771 34176 y FO(=)336 b FG(S)34863 33587 y FF(])34793
34523 y FB(1)11290 36275 y FO(=)-202 b FI(\))13243 36457
y FB(2)14105 36275 y FO(=)270 b(=)-202 b FI(\))17271
36457 y FB(1)29955 36275 y FO(=)g FI(\))31908 35686 y
FF(])31908 36622 y FB(2)32771 36275 y FO(=)269 b(=)-202
b FI(\))35936 35686 y FF(])35936 36622 y FB(1)11290 38374
y FI(\241)g(!)13243 38556 y FB(2)14105 38374 y FO(=)270
b FI(\241)-203 b(!)17270 38556 y FB(1)18133 38374 y FI([)269
b(f)p FO(\()p FG(v)20875 38556 y FB(1)21401 38374 y FG(;)202
b(v)22528 38556 y FB(2)23053 38374 y FO(\))p FI(g)5825
b(\241)-202 b(!)31908 37785 y FF(])31908 38722 y FB(2)32771
38374 y FO(=)269 b FI(\241)-203 b(!)35935 37785 y FF(])35935
38722 y FB(1)4253 41569 y FI(\262)607 b FO(Primanje)404
b(p)34 b(oruk)-34 b(e)5466 43075 y(Op)34 b(et)450 b FG(v)9164
43257 y FB(2)10103 43075 y FI(2)413 b FG(S)12137 42485
y FF(])12067 43422 y FB(1)12893 43075 y FI(n)301 b FG(S)14543
43257 y FB(1)15519 43075 y FO(prima)450 b(p)34 b(oruku)451
b FG(m)f FO(o)34 b(d)450 b FG(v)27160 43257 y FB(1)28099
43075 y FI(2)414 b FG(S)30064 43257 y FB(1)30590 43075
y FO(;)473 b(no)451 b(o)-34 b(v)-67 b(a)67 b(j)450 b(puta)i(p)34
b(osto)67 b(ji)5466 44737 y FG(v)421 b FI(2)377 b FG(S)8403
44919 y FB(1)9358 44737 y FO(tak)-67 b(a)-34 b(v)429
b(da)g FG(v)421 b FO(=)-202 b FI(\))17319 44148 y FF(])17319
45084 y FB(1)18223 44737 y FG(v)18811 44919 y FB(2)19336
44737 y FO(.)612 b(Do)34 b(da)67 b(jemo)430 b FG(v)26740
44919 y FB(2)27694 44737 y FO(u)f FG(S)29539 44919 y
FB(2)30065 44737 y FO(,)435 b(to)429 b(zna)-34 b(\267)-572
b(ci)428 b(da)i(je)e(primiio)5466 46243 y FG(m)p FO(,)404
b(i)f(uklju)-34 b(\267)-572 b(cujemo)405 b(ulazni)f(=)-202
b FI(\))p FO(-brid:)12500 48943 y FG(S)13243 49125 y
FB(2)14105 48943 y FO(=)337 b FG(S)16128 49125 y FB(1)16923
48943 y FI([)539 b(f)p FG(v)19464 49125 y FB(2)19990
48943 y FI(g)10569 b FG(S)31978 48354 y FF(])31908 49291
y FB(2)32771 48943 y FO(=)336 b FG(S)34863 48354 y FF(])34793
49291 y FB(1)11290 51043 y FO(=)-202 b FI(\))13243 51225
y FB(2)14105 51043 y FO(=)270 b(=)-202 b FI(\))17271
51225 y FB(1)18402 51043 y FI(f)p FO(\()p FG(v)43 b(;)202
b(v)21237 51225 y FB(2)21763 51043 y FO(\))p FI(g)7115
b FO(=)-202 b FI(\))31908 50453 y FF(])31908 51390 y
FB(2)32771 51043 y FO(=)269 b(=)-202 b FI(\))35936 50453
y FF(])35936 51390 y FB(1)11290 53142 y FI(\241)g(!)13243
53324 y FB(2)14105 53142 y FO(=)270 b FI(\241)-203 b(!)17270
53324 y FB(1)18133 53142 y FI([)269 b(f)p FO(\()p FG(v)20875
53324 y FB(1)21401 53142 y FG(;)202 b(v)22528 53324 y
FB(2)23053 53142 y FO(\))p FI(g)5825 b(\241)-202 b(!)31908
52552 y FF(])31908 53489 y FB(2)32771 53142 y FO(=)269
b FI(\241)-203 b(!)35935 52552 y FF(])35935 53489 y FB(1)4253
56337 y FI(\262)607 b FO(Kreiranje)403 b(no)-34 b(v)g(e)405
b(niti)f(instancira)67 b(ju)-34 b(\266)-572 b(ci)405
b(njene)f(svje)-34 b(\267)-572 b(ze)404 b(vrijednosti)5466
57842 y(Nek)-67 b(a)369 b(je)h FG(s)g FO(parametrizirana)f(nit)h(iz)g
(prostora)g(niti)g FI(S)91 b FO(.)527 b(Uv)-34 b(o)34
b(dimo)370 b(tu)h(no)-34 b(vu)370 b(nit)5466 59348 y(instancira)67
b(ju)-34 b(\266)-572 b(ci)445 b(njene)g(parametre)f(k)-34
b(o)67 b(ji)445 b(su)f(ozna)-34 b(\267)-572 b(ceni)445
b(da)f(jedinstv)-34 b(eno)446 b(izviru)5466 60853 y(na)470
b(to)67 b(j)471 b(niti,)487 b(primjenjuju)-34 b(\266)-572
b(ci)472 b(supstituciju)g FG(\273)526 b FO(k)-34 b(o)67
b(ja)471 b(preslik)-67 b(a)-34 b(v)-67 b(a)469 b(te)h(parametre)5466
62358 y(u)404 b(k)-34 b(onstan)g(te)406 b(nek)-34 b(ori)-64
b(\267)-542 b(stene)404 b(u)h(\()p FG(\276)20620 62540
y FB(1)21145 62358 y FG(;)202 b(\276)22420 61769 y FF(])22377
62706 y FB(1)22903 62358 y FO(\).)538 b(Imamo:)14114
65216 y FG(\276)14807 65398 y FB(2)15669 65216 y FO(=)336
b FG(\276)17641 65398 y FB(1)26815 65216 y FG(\276)27551
64626 y FF(])27508 65563 y FB(2)28370 65216 y FO(=)g
FG(\276)30385 64626 y FF(])30342 65563 y FB(1)31137 65216
y FI([)539 b FG(\273)56 b(s)5466 67917 y FO(No)-34 b(v)-67
b(a)404 b(nit)g(je)g(spremna)h(za)f(k)-34 b(ori)-64 b(\267)-542
b(stenje,)404 b(p)34 b(o)-34 b(\267)-572 b(cetak)403
b(k)-34 b(om)g(unik)-67 b(acije.)4253 70411 y FI(\262)607
b FO(Stv)-67 b(aranje)404 b(p)34 b(otpuno)406 b(instancirane)e(niti)
5466 71916 y(Ovdje)318 b(sp)34 b(eci\257ciramo)317 b(svrh)-34
b(u)318 b(no)-34 b(v)g(ogenerirane)318 b(niti,)335 b(instancira)67
b(ju)-34 b(\266)-572 b(ci)319 b(preostale)21755 74956
y(57)p eop end end
%%Page: 58 58
TeXDict begin HPSdict begin 58 57 bop 10779 7181 a FO(parametre.)1036
b(Nek)-67 b(a)570 b(je)g FG(\273)56 b(s)570 b FO(parcijalno)h
(instancirana)f(parametrizirana)g(nit,)10779 8687 y(k)-67
b(ao)458 b(ona)h(iz)e(pretho)34 b(dnog)460 b(slu)-34
b(\267)-572 b(ca)67 b(ja.)702 b(Nek)-67 b(a)458 b(je)g
FG(\265)492 b FO(p)34 b(otpuna)460 b(supstitucija)g(za)e(tu)10779
10192 y(nit.)663 b(T)-101 b(a)445 b(supstitucija)i(mora)e(biti)h(k)-34
b(ompatibilna)446 b(s)g(restrik)-34 b(cijama)444 b(danim)i(uz)10779
11698 y(inicijalizaciju)403 b(niti,)h(ak)-34 b(o)404
b(ih)g FG(\273)56 b(s)405 b FO(sp)34 b(ominje.)539 b(Imamo)17921
14141 y FG(\276)18614 14323 y FB(2)19476 14141 y FO(=)337
b FG(\276)21449 14323 y FB(1)29116 14141 y FG(\276)29852
13551 y FF(])29809 14488 y FB(2)30671 14141 y FO(=)g
FG(\276)32687 13551 y FF(])32644 14488 y FB(1)33438 14141
y FI(\241)269 b FG(\273)56 b(s)270 b FI([)539 b FG(\265)34
b FO(\()p FG(\273)56 b(s)p FO(\))p FG(:)7749 17296 y
FL(De\257nicija)465 b(23)606 b FK(A)-31 b(ko)482 b(u)i(pr)-62
b(ostoru)481 b(niti)j FI(S)574 b FK(kon\257gur)-62 b(acija)481
b FO(\()p FG(\276)36489 17478 y FB(2)37015 17296 y FG(;)202
b(\276)38290 16707 y FF(])38247 17644 y FB(2)38772 17296
y FO(\))485 b FK(nep)-62 b(osr)g(e)g(dno)482 b(sli-)7749
18959 y(je)-62 b(di)308 b(kon\257gur)-62 b(aciju)307
b FO(\()p FG(\276)18159 19141 y FB(1)18685 18959 y FG(;)202
b(\276)19960 18369 y FF(])19917 19306 y FB(1)20442 18959
y FO(\))p FK(,)335 b(ka)-62 b(\267)-558 b(zemo)308 b(da)g(p)-62
b(ostoji)431 b FO(p)34 b(otez)310 b FG(o)f FK(koji)f(tr)-62
b(ansformir)g(a)308 b FO(\()p FG(\276)45546 19141 y FB(1)46072
18959 y FG(;)202 b(\276)47347 18369 y FF(])47304 19306
y FB(1)47829 18959 y FO(\))7749 20621 y FK(u)531 b FO(\()p
FG(\276)10095 20803 y FB(2)10620 20621 y FG(;)202 b(\276)11895
20032 y FF(])11852 20969 y FB(2)12378 20621 y FO(\))p
FK(,)555 b(u)531 b(smislu)623 b FO(nep)34 b(osrednog)511
b(prijelaza)p FK(.)850 b(T)-93 b(o)531 b(ozna)-31 b(\267)-589
b(cavamo)528 b FO(\()p FG(\276)41688 20803 y FB(1)42214
20621 y FG(;)202 b(\276)43489 20032 y FF(])43446 20969
y FB(1)43971 20621 y FO(\))45705 19934 y FF(o)44956 20621
y FI(7\241)-202 b(!)46909 20809 y FE(S)7749 22284 y FO(\()p
FG(\276)8913 22466 y FB(2)9439 22284 y FG(;)202 b(\276)10714
21694 y FF(])10671 22631 y FB(2)11196 22284 y FO(\))p
FK(.)1130 b(A)-31 b(ko)623 b(iz)h FO(\()p FG(\276)18496
22466 y FB(1)19022 22284 y FG(;)202 b(\276)20297 21694
y FF(])20254 22631 y FB(1)20779 22284 y FO(\))625 b FK(mo)-62
b(\267)-558 b(zemo)623 b(sti)-31 b(\266)-589 b(ci)623
b FO(\()p FG(\276)30762 22466 y FB(2)31288 22284 y FG(;)202
b(\276)32563 21694 y FF(])32520 22631 y FB(2)33045 22284
y FO(\))625 b FK(u)f(nekom)g(kona)-31 b(\267)-589 b(cnom)623
b(nizu)7749 23993 y(p)-62 b(oteza,)403 b(tada)396 b(se)i(r)-62
b(adi)398 b(o)474 b FO(prijelazu)366 b(u)g(vi)-64 b(\267)-542
b(se)366 b(k)-34 b(orak)-67 b(a)p FK(,)342 b(\267)-558
b(sto)398 b(ozna)-31 b(\267)-589 b(cavamo)395 b FO(\()p
FG(\276)41865 24175 y FB(1)42391 23993 y FG(;)202 b(\276)43666
23403 y FF(])43623 24340 y FB(1)44148 23993 y FO(\))45705
23306 y FF(o)44956 23993 y FI(7\241)-202 b(!)46909 23154
y FE(\244)46909 24292 y(S)7749 25655 y FO(\()p FG(\276)8913
25837 y FB(2)9439 25655 y FG(;)202 b(\276)10714 25066
y FF(])10671 26002 y FB(2)11196 25655 y FO(\))p FK(.)9631
28209 y FO(O)-34 b(\267)-572 b(cito)422 b(je)h(da)g(sv)-67
b(aki)422 b(p)34 b(otez)423 b(iz)f(k)-34 b(on\257guracije)423
b(v)-34 b(o)34 b(di)423 b(p)34 b(ono)-34 b(v)g(o)424
b(u)f(k)-34 b(on\257guraciju,)429 b(pa)7749 29714 y(je)404
b(i)g(rezultat)g(prijelaza)f(u)i(vi)-64 b(\267)-542 b(se)403
b(k)-34 b(orak)-67 b(a)403 b(tak)-34 b(o)p 29104 29101
364 53 v(der)405 b(uvijek)f(k)-34 b(on\257guracija.)9631
32725 y(De\257nicija)455 b(22)h(dala)f(nam)h(je)g(i)f(vi)-64
b(\267)-542 b(se:)641 b(mehanizam)455 b(supstituiranja)j(parametara)
7749 34231 y(niti)404 b(i)g(na)-34 b(\267)-572 b(cin)404
b(instanciranja)h(svje)-34 b(\267)-572 b(zih)404 b(vrijednosti.)7749
38006 y FH(5.2)1792 b(Prilago)p 17806 37189 538 71 v(da)-50
b(v)-100 b(anje)877 b(mo)50 b(dela)876 b(transformacija)h(m)-50
b(ulti-)11833 39998 y(skup)50 b(o)-50 b(v)-100 b(a)7749
42704 y FO(Malo)370 b(\266)-572 b(cemo)403 b(mo)34 b(di\257cirati)404
b(teorije)g(roli)f(da)i(bi)f(ih)g(pribli)-34 b(\267)-572
b(zili)402 b(nitima.)7749 44210 y(Prv)-34 b(o,)494 b(de\257niramo)478
b FK(r)-62 b(e)g(gularne)566 b FO(protok)-34 b(olsk)g(e)477
b(teorije)g(k)-67 b(ao)476 b(protok)-34 b(olsk)g(e)477
b(teorije)g(k)-34 b(o)67 b(je)7749 45715 y(zado)-34 b(v)g(olja)g(v)-67
b(a)67 b(ju)446 b(sljede)-34 b(\266)-572 b(ci)445 b(uvjet:)621
b(svi)444 b(p)34 b(erzisten)-34 b(tni)445 b(p)34 b(o)g(daci)445
b(k)-34 b(o)67 b(ji)445 b(se)g(k)-34 b(oriste)445 b(u)g(nek)-34
b(o)67 b(j)7749 47221 y(roli)535 b FG(\275)h FO(mora)67
b(ju)538 b(biti)e(istakn)-34 b(uti)538 b(u)e(pra)-34
b(vilu)537 b(kreiranja)f(te)g(role,)568 b FG(r)38756
47403 y FF(\275)p FB(0)39764 47221 y FO(.)935 b(Nak)-34
b(on)537 b(toga,)7749 48726 y(p)34 b(erzisten)-34 b(tne)433
b(informacije)g(se)g(vi)-64 b(\267)-542 b(se)432 b(ne)h(p)34
b(o)67 b(ja)-34 b(vljuju)436 b(u)d(pra)-34 b(vilima)432
b(k)-34 b(o)67 b(ji)434 b(slijede)f(za)f(tu)7749 50231
y(rolu)404 b({)g(sv)-34 b(e)404 b(je)g(zapam)-34 b(\266)-572
b(ceno)404 b(inicijalizacijom)15823 52674 y FG(r)16370
52856 y FF(\275)p FB(0)17512 52674 y FO(:)741 b FG(\274)43
b FO(\()-16 b FG(~)-590 b(x)p FO(\))337 b FI(\241)-202
b(!)337 b FN(A)24394 52856 y FF(\275)p FB(0)25401 52674
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%%Page: 59 59
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%%Page: 60 60
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b(teorije)7749 50552 y FO(Napada)-34 b(\267)-572 b(cev)-67
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b Fx(I)p Fy(\()p Fw(m)p Fy(\))9291 57288 y(dcmp)11935
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b(m)30750 57454 y Fr(2)31247 57288 y Ft(i)p Fy(\))1108
b Ft(\241)-184 b(!)1107 b Fx(I)p Fy(\()p Fw(m)37815 57454
y Fr(1)38312 57288 y Fy(\))p Fw(;)370 b Fx(I)p Fy(\()p
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y(decr)11324 58215 y Fh(0)13476 58616 y Fy(:)1476 b Fx(I)p
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58616 y Fw(;)184 b(k)31161 58782 y Fv(d)31678 58616 y
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58782 y Fv(e)44042 58616 y Fw(;)184 b(k)45109 58782 y
Fv(d)45627 58616 y Fy(\))9291 59945 y(snd)10958 59543
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Fy(\))9291 61273 y(cmp)11320 60871 y Fh(0)13476 61273
y Fy(:)12375 b Fx(I)p Fy(\()p Fw(m)27867 61439 y Fr(1)28364
61273 y Fy(\))p Fw(;)370 b Fx(I)p Fy(\()p Fw(m)31180
61439 y Fr(2)31678 61273 y Fy(\))1107 b Ft(\241)-184
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61273 y Fw(;)184 b(m)40206 61439 y Fr(2)40703 61273 y
Ft(i)p Fy(\))9291 62602 y(encr)11324 62200 y Fh(0)13476
62602 y Fy(:)13288 b Fx(I)p Fy(\()p Fw(m)p Fy(\))p Fw(;)371
b Fx(I)p Fy(\()p Fw(k)31201 62768 y Fv(e)31678 62602
y Fy(\))1107 b Ft(\241)-184 b(!)1107 b Fx(I)p Fy(\()p
Fw(m)p Fy(\))p Fw(;)371 b Fx(I)p Fy(\()p Fx(enc)q Fy(\()p
Fw(k)42223 62768 y Fv(e)42699 62602 y Fw(;)184 b(m)p
Fy(\)\))9291 63930 y(nnc)11013 63528 y Fh(0)13476 63930
y Fy(:)19432 b Ft(\241)-184 b(!)1107 b(9)p Fw(n)184 b
Fx(I)p Fy(\()p Fw(m)p Fy(\))9291 65258 y(p)31 b(ers)11300
64857 y Fh(0)13476 65258 y Fy(:)15822 b Fw(\274)40 b
Fy(\()p Fw(m)p Fy(\))1107 b Ft(\241)-184 b(!)1107 b Fx(I)p
Fy(\()p Fw(m)p Fy(\))p Fw(;)371 b(\274)40 b Fy(\()p Fw(m)p
Fy(\))9291 66587 y(dup)2340 b(:)16185 b Fx(I)p Fy(\()p
Fw(m)p Fy(\))1108 b Ft(\241)-184 b(!)1107 b Fx(I)p Fy(\()p
Fw(m)p Fy(\))p Fw(;)371 b Fx(I)p Fy(\()p Fw(m)p Fy(\))9291
67915 y(del)2771 b(:)16185 b Fx(I)p Fy(\()p Fw(m)p Fy(\))1108
b Ft(\241)-184 b(!)1107 b(\242)16720 71681 y FO(Slik)-67
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74956 y FO(60)p eop end end
%%Page: 61 61
TeXDict begin HPSdict begin 61 60 bop 4317 7181 a FO(O)-34
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b(teorije)g FI(I)89 b FO(,)610 b(k)-34 b(onstruk)g(cija)570
b(niza)2435 14759 y(pra)-34 b(vila)388 b(k)-34 b(o)67
b(ji,)392 b(umjesto)d(pra)-34 b(vila)388 b(iz)f FI(I)478
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b(slijedi.)4317 19327 y(U)493 b(drugom)g(smjeru,)514
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b(tvrdnja)g(leme)e(10.)2435 25476 y FL(Lema)464 b(10)606
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b(te)-62 b(orija,)432 b(i)h FG(S)26159 25658 y FB(1)27119
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b(da)g FG(S)22156 28363 y FB(1)23770 27494 y FF(r)23019
28181 y FI(\241)-202 b(!)24972 27342 y FE(\244)24972
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30315 y(da)432 b FG(S)7881 30497 y FB(1)9346 29628 y
FF(r)9797 29315 y FD(0)8744 30315 y FI(\241)-202 b(!)10697
29176 y FE(\244)10697 30615 y(R)p FF(;)p FE(I)12339 30362
y FD(0)13031 30315 y FG(S)13774 30497 y FB(2)3868 33648
y FK(2.)606 b(za)514 b(svaki)f(niz)h(pr)-62 b(avila)513
b FG(r)16919 33208 y FE(0)17744 33648 y FK(takav)g(da)h
FG(S)23513 33830 y FB(1)25124 32961 y FF(r)25575 32649
y FD(0)24523 33648 y FI(\241)-203 b(!)26475 32509 y FE(\244)26475
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y FG(S)29699 33830 y FB(2)30740 33648 y FK(p)-62 b(ostoji)512
b(niz)j(pr)-62 b(avila)513 b FG(r)548 b FK(i)5466 35482
y(uljezovo)430 b(stanje)i FG(I)14271 35042 y FE(0)15016
35482 y FK(takvi)f(da)i FG(S)20374 35664 y FB(1)21988
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y FE(\244)23190 35782 y(R)p FF(;)p FE(I)25225 35482 y
FG(S)25968 35664 y FB(2)26494 35482 y FK(.)2435 38570
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b(o)434 b(pra)-34 b(vilo)434 b(iz)g FI(I)13653 39635
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b(je)435 b(imitiramo)2435 41581 y(pra)-34 b(vilom)310
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b(vilo)310 b FG(snd)p FO(,)328 b(ne)310 b(moramo)h(ni)-64
b(\267)-542 b(sta)310 b(drugo)h(napra)-34 b(viti)311
b(nego)2435 43086 y(primjeniti)418 b(paralelno)e(pra)-34
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b FG(I)16366 45657 y FE(0)16677 46097 y FO(.)538 b(Ostatak)405
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b(ci:)2435 54925 y FL(Korolar)464 b(3)606 b FK(Neka)309
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b(stanje,)2435 56431 y FG(S)439 b FK(neko)367 b(stanje,)380
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64367 y FI(\241)-202 b(!)11228 63228 y FE(\244)11228
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y FG(\273)14352 64060 y FO(\271)14148 64367 y FG(S)477
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FG(S)6209 66382 y FB(0)7822 65513 y FF(r)7071 66200 y
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71916 y(lem)-34 b(u)405 b(10,)e(dobijamo)j(ono)340 b(\267)-542
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%%Page: 62 62
TeXDict begin HPSdict begin 62 61 bop 7749 7181 a FH(5.3)1792
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b(niti.)7749 20472 y FL(T)-116 b(ransformacija)462 b(protok)-39
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b FG(s)13367 31405 y FF(\275)14208 31223 y FO(je)g(parametrizirana)g
(sa)287 b FG(~)-590 b(x;)192 b(~)-596 b(y)43 b(;)170
b(~)-574 b(n)303 b FO(gdje)g(su)h(v)-67 b(arijable)286
b FG(~)-590 b(x)303 b FO(sp)34 b(omen)-34 b(ute)305 b(me)p
46513 30609 V(du)10779 32729 y(p)34 b(erzisten)-34 b(tnim)291
b(\267)-572 b(cinjenicama)323 b FG(\274)43 b FO(\()-16
b FG(~)-590 b(x)p FO(\),)308 b FG(~)-574 b(n)323 b FO(su)i(v)-67
b(arijable)322 b(egzistencijalno)i(kv)-67 b(an)-34 b(ti\257-)10779
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b(role)f FG(\275)p FO(,)312 b FG(~)-596 b(y)345 b FO(su)301
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b FI(\))337 b FG(v)20179 53892 y FF(j)21069 53710 y FO(akk)-34
b(o)404 b FG(j)i FO(=)337 b FG(i)269 b FO(+)g(1.)9631
56150 y(Na)383 b(o)-34 b(v)-67 b(a)67 b(j)383 b(na)-34
b(\267)-572 b(cin)384 b(prev)-34 b(o)34 b(dimo)382 b(teoriju)i
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FO(.)7749 59340 y FL(Predsta)-39 b(vljanje)464 b(stanja)g(k)-39
b(on\257guracijama)7749 61629 y FO(Dosad)510 b(smo)g(usp)34
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b(cki)510 b(dio)f(opisa)h(protok)-34 b(ola,)537 b(ono)446
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b(stanje)h FG(S)407 b FO(=)336 b(\246)201 b FI(])g FG(I)95
b FO(\()33971 64319 y FG(~)33679 64639 y(m)34743 64289
y FE(0)35055 64639 y FO(\))201 b FI(])g FG(N)132 b FO(\()k
FG(~)-742 b(m)r FO(\))201 b FI(])g FG(A)371 b FO(m)-34
b(ultiskup)7749 66145 y(p)34 b(erzisten)-34 b(tnih)367
b(\267)-572 b(cinjenica,)366 b(\267)-572 b(cinjenica)399
b(k)-34 b(o)67 b(je)401 b(ozna)-34 b(\267)-572 b(ca)-34
b(v)-67 b(a)67 b(ju)401 b(predik)-67 b(ate)399 b(roli,)366
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b FI(])g FG(I)95 b FO(\()25997 70091 y FG(~)25705 70411
y(m)26769 70061 y FE(0)27080 70411 y FO(\))295 b FI(])f
FG(N)132 b FO(\()k FG(~)-742 b(m)p FO(\))294 b FI(])g
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71916 y(\257gur)-62 b(acijom)431 b(niti)j FO(\()p FG(\276)-24
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b FK(ako:)27068 74956 y FO(62)p eop end end
%%Page: 63 63
TeXDict begin HPSdict begin 63 62 bop 4253 7181 a FI(\262)607
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y FE(0)28907 36741 y FO(\()p FG(m)p FO(\))p FA(q)337
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56732 y FO(\()p FI(\242)p FG(;)202 b FI(\242)p FO(\))18649
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%%Page: 64 64
TeXDict begin HPSdict begin 64 63 bop 7749 7181 a FO(sa)519
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b(v)g(e)404 b(teorije.)9631 37886 y(Nak)-34 b(on)278
b(\267)-542 b(sto)343 b(napra)-34 b(vimo)342 b(tak)-67
b(a)-34 b(v)342 b(prijev)-34 b(o)34 b(d,)354 b(u)343
b(mogu)-34 b(\266)-572 b(cnosti)343 b(smo)f(dok)-67 b(azati)342
b(teorem)7749 39391 y(k)-34 b(o)67 b(jim)316 b(se)f(tvrdi)g(da,)334
b(un)-34 b(utar)317 b(opisane)f(translacije,)332 b(tranzicije)315
b(o)34 b(dgo)-34 b(v)-67 b(ara)67 b(ju)317 b(k)-34 b(oracima)7749
40897 y(me)p 9558 40283 V(du)404 b(k)-34 b(on\257guracijama)406
b(niti.)7749 44042 y FL(Prev)-39 b(o)p 11578 43421 419
54 v(denje)465 b(parametriziranih)f(niti)i(u)f(role)7749
46331 y FO(Pretp)34 b(osta)-34 b(vimo)568 b(da)f(nam)h(je)g(dana)g(nit)
g FG(s)g FO(prostora)g(niti)f FI(S)91 b FO(,)608 b(tada)568
b(k)-34 b(onstruiramo)7749 47836 y(teoriju)404 b(roli)f
FA(p)p FI(S)91 b FA(q)404 b FO(na)h(sljede)-34 b(\266)-572
b(ci)403 b(na)-34 b(\267)-572 b(cin:)9567 50043 y FI(\262)606
b FO(Zap)34 b(o)-34 b(\267)-572 b(cinje)404 b(s)g(pra)-34
b(vilom)404 b(kreiranja)g(role)23366 52412 y FG(\274)43
b FO(\()-16 b FG(~)-590 b(x)q FO(\))337 b FI(\241)-203
b(!)337 b FN(A)29170 52594 y FF(s)p FB(0)30131 52412
y FO(\()-16 b FG(~)-590 b(x)p FO(\))p FG(;)202 b(\274)43
b FO(\()-16 b FG(~)-590 b(x)q FO(\))p FG(;)10779 54781
y FO(gdje)438 b(su)422 b FG(~)-590 b(x)437 b FO(v)-34
b(e)g(\266)-572 b(c)437 b(isk)-34 b(ori)-64 b(\267)-542
b(stene)437 b(v)-67 b(arijable)436 b(me)p 30983 54167
364 53 v(du)i(onima)g(deklariranima)e(pri)h(ini-)10779
56286 y(cijalizaciji)456 b(niti)i FG(s)p FO(.)699 b(P)-34
b(erzisten)g(tni)458 b(p)34 b(o)g(daci)458 b(su)g(k)-67
b(ao)457 b(i)g(obi)-34 b(\267)-572 b(cno:)646 b(ja)-34
b(vni)458 b(klju)-34 b(\267)-572 b(cevi,)10779 57791
y(o)34 b(dnosno)405 b(imena)f(agenata.)9567 60175 y FI(\262)606
b FO(Za)368 b(sv)-67 b(aki)367 b(vrh)h FG(v)18239 60357
y FF(i)18982 60175 y FO(obilje)-34 b(\267)-572 b(zen)368
b(sa)h(+)p FG(m)p FO(\()-16 b FG(~)-590 b(x;)170 b(~)-574
b(n)o FO(\),)375 b(gdje)369 b(su)336 b FG(~)-573 b(n)367
b FO(v)-67 b(arijable)368 b(soli,)374 b(nek)-34 b(e)368
b(o)34 b(d)10779 61681 y(v)-67 b(arijabli)410 b(za)h(k)-34
b(o)67 b(je)412 b(se)e(k)-34 b(o)34 b(d)412 b(instanciranja)g(zah)-34
b(tjev)-67 b(alo)411 b(jedinstv)-34 b(eno)412 b(izviranje,)10779
63186 y(imamo)19231 64692 y FN(A)20039 64874 y FF(si)20850
64692 y FO(\()-16 b FG(~)-590 b(x)p FO(\))337 b FI(\241)-202
b(!)336 b(9)-32 b FG(~)-574 b(n)270 b FN(A)27590 64874
y FF(si)p FB(+1)29603 64692 y FO(\()-16 b FG(~)-590 b(x;)170
b(~)-574 b(n)o FO(\))p FG(;)202 b FN(N)p FO(\()p FG(m)p
FO(\()-16 b FG(~)-590 b(x)q(;)170 b(~)-574 b(n)o FO(\)\))p
FG(:)9567 67179 y FI(\262)606 b FO(Za)404 b(sv)-67 b(aki)403
b(vrh)h FG(v)18347 67361 y FF(i)19126 67179 y FO(obilje)-34
b(\267)-572 b(zen)404 b(sa)g FI(\241)p FG(m)p FO(\()-16
b FG(~)-590 b(x;)192 b(~)-596 b(y)44 b FO(\))404 b(imamo)g(pra)-34
b(vilo)404 b(slanja)20156 69547 y FN(A)20964 69729 y
FF(si)21775 69547 y FO(\()-16 b FG(~)-590 b(x)p FO(\))p
FG(;)202 b FN(N)p FO(\()p FG(m)p FO(\()-16 b FG(~)-590
b(x;)192 b(~)-596 b(y)44 b FO(\)\))337 b FI(\241)-202
b(!)337 b FN(A)33061 69729 y FF(si)p FB(+1)35074 69547
y FO(\()-16 b FG(~)-590 b(x;)192 b(~)-596 b(y)44 b FO(\))p
FG(;)10779 71916 y FO(gdje)405 b(su)394 b FG(~)-596 b(y)448
b FO(nek)-34 b(e)404 b(o)34 b(d)404 b(dosad)h(neisk)-34
b(ori)-64 b(\267)-542 b(stenih)404 b(v)-67 b(arijabli.)27068
74956 y(64)p eop end end
%%Page: 65 65
TeXDict begin HPSdict begin 65 64 bop 2435 7181 a FO(Uo)-34
b(\267)-572 b(cimo)361 b(da)h(je)g(teorija)f FA(p)p FI(S)91
b FA(q)362 b FO(regularna)f(teorija)g(roli)g({)g(translacija)h(je)f
(mogla)h(biti)f(i)g(u)2435 8687 y(normaln)-34 b(u)425
b(teoriju,)j(ali)423 b(tada)i(bi)e(k)-34 b(omplicirali)422
b(dobiv)-67 b(anje)424 b(prv)-34 b(og)424 b(pra)-34 b(vila,)428
b(za)423 b(k)-34 b(o)67 b(jeg)2435 10192 y(bi)404 b(p)34
b(osto)67 b(jale)405 b(dvije)f(op)34 b(cije.)2435 13384
y FL(Prev)-39 b(o)p 6264 12763 419 54 v(denje)465 b(k)-39
b(on\257guracija)465 b(u)g(stanja)2435 15673 y FO(P)-34
b(oznato)67 b(j)595 b(k)-34 b(on\257guraciji)595 b(\()p
FG(\276)-24 b(;)202 b(\276)17270 15233 y FF(])17691 15673
y FO(\))594 b(nad)g(prostorom)g(niti)g FI(S)91 b FO(,)641
b(pridru)-34 b(\267)-572 b(zujemo)594 b(stanje)2435 17178
y FG(S)3178 17366 y FE(S)3869 17178 y FO(\()p FG(\276)-24
b(;)202 b(\276)6284 16738 y FF(])6705 17178 y FO(\))337
b(=)f(\246)270 b FI(])f FG(I)365 b FI(])269 b FG(N)401
b FI(])270 b FG(A)p FO(:)4253 19629 y FI(\262)607 b FO(\246)497
b(je)f(dobiv)-34 b(en)498 b(sakupljanjem)g(svih)f(p)34
b(erzisten)-34 b(tnih)498 b(p)34 b(o)g(datak)-67 b(a)497
b(iz)f FG(\276)37843 19189 y FF(])38264 19629 y FO(,)520
b(nak)-34 b(on)5402 21135 y(\267)-542 b(sto)404 b(su)h(v)-34
b(e)g(\266)-572 b(c)403 b(instancirani;)4253 23616 y
FI(\262)607 b FO(m)-34 b(ultiskupu)345 b FG(A)e FO(do)34
b(damo)345 b FN(A)18355 23798 y FF(i)18731 23616 y FO(\()19126
23393 y FG(~)19202 23616 y(t)p FO(\))f(sv)-67 b(aki)342
b(put)j(k)-67 b(ad)343 b(imamo)h FG(v)32289 23798 y FF(i)p
FE(\241)p FB(1)34203 23616 y FO(=)-202 b FI(\))337 b
FG(v)37081 23798 y FF(i)37799 23616 y FO(u)344 b FG(\276)39552
23176 y FF(])40122 23616 y FI(\241)148 b FG(\276)43 b
FO(,)5466 25122 y FG(v)6054 25304 y FF(i)p FE(\241)p
FB(1)7968 25122 y FI(2)337 b FG(\276)43 b FO(;)4253 27603
y FI(\262)607 b FG(N)478 b FO(je)347 b(m)-34 b(ultiskup)347
b(svih)g FN(N)p FO(\()p FG(m)p FO(\))g(p)34 b(oruk)-67
b(a)346 b FG(m)g FO(k)-34 b(o)67 b(je)347 b(su)g(p)34
b(oslane,)358 b(a)346 b(nisu)h(primljene,)5466 29109
y(tj.)423 b(takvih)g(da)g(p)34 b(osto)67 b(ji)424 b(vrh)e
FG(v)19423 29291 y FF(i)20166 29109 y FI(2)368 b FG(\276)466
b FO(na)423 b(regularno)67 b(j)423 b(niti,)428 b(obilje)-34
b(\267)-572 b(zen)422 b(sa)h(+)p FG(m)p FO(,)k(i)5466
30614 y(nema)404 b FI(\241)-202 b(!)p FO(-brida)404 b(iz)g
FG(v)16091 30796 y FF(i)16870 30614 y FO(u)g FG(\276)43
b FO(;)4253 33096 y FI(\262)607 b FG(I)612 b FO(je,)545
b(sli)-34 b(\267)-572 b(cno)517 b(k)-67 b(ao)517 b FG(N)132
b FO(,)545 b(m)-34 b(ultiskup)485 b(\267)-572 b(cinjenica)517
b FN(I)p FO(\()p FG(m)p FO(\),)546 b(za)517 b(sv)-34
b(e)517 b FG(m)h FO(k)-34 b(o)67 b(je)518 b(je)f(uljez)5466
34601 y(p)34 b(oslao,)459 b(a)448 b(nije)g(primio)g(u)h
FG(\276)491 b FO(\(jer)449 b(tak)-34 b(o)449 b(uljez)f(pam)-34
b(ti)449 b(p)34 b(o)g(datk)-34 b(e,)459 b(k)-34 b(onstan)g(tnim)5466
36107 y(slanjem)404 b(i)g(primanjem\).)2435 39299 y FL(P)-39
b(o)g(v)g(eziv)-77 b(anje)464 b(uljezo)-39 b(vih)465
b(niti)h(i)e(uljezo)-39 b(v)g(e)465 b(teorije)2435 41587
y FO(Preslik)-67 b(a)-34 b(v)-67 b(amo)403 b(uljezo)-34
b(v)g(e)404 b(niti)g(u)g(uljezo)-34 b(v)-67 b(a)404 b(pra)-34
b(vila:)4072 44249 y FA(p)p FG(S)70 b(ep)p FO(\()p FG(m)8200
44431 y FB(1)8727 44249 y FG(;)202 b(m)10330 44431 y
FB(2)10856 44249 y FO(\))p FA(q)337 b FO(=)606 b(dcmp)16714
43749 y FE(0)17025 44249 y FO(\()p FG(m)18560 44431 y
FB(1)19087 44249 y FG(;)202 b(m)20690 44431 y FB(2)21215
44249 y FO(\))1427 b FA(p)p FG(C)87 b(onc)p FO(\()p FG(m)28048
44431 y FB(1)28573 44249 y FG(;)202 b(m)30176 44431 y
FB(2)30702 44249 y FO(\))p FA(q)337 b FO(=)606 b(cmp)35887
43749 y FE(0)36198 44249 y FO(\()p FG(m)37733 44431 y
FB(1)38259 44249 y FG(;)202 b(m)39862 44431 y FB(2)40388
44249 y FO(\))3862 46087 y FA(p)p FG(D)34 b(ec)p FO(\()p
FG(m;)202 b(k)38 b(;)202 b(k)10546 45586 y FE(0)10856
46087 y FO(\))p FA(q)337 b FO(=)606 b(decr)16045 45586
y FE(0)16355 46087 y FO(\()p FG(m;)202 b(k)38 b(;)202
b(k)20306 45586 y FE(0)20617 46087 y FO(\))4048 b FA(p)p
FG(E)70 b(nc)p FO(\()p FG(m;)202 b(k)38 b FO(\))p FA(q)336
b FO(=)606 b(encr)35891 45586 y FE(0)36201 46087 y FO(\()p
FG(m;)202 b(k)38 b FO(\))6373 47924 y FA(p)p FG(D)c(up)p
FO(\()p FG(m)p FO(\))p FA(q)337 b FO(=)606 b(dup)15838
47424 y FE(0)16150 47924 y FO(\()p FG(m)p FO(\))7111
b FA(p)p FG(F)168 b(l)24 b(ush)p FO(\()p FG(m)p FO(\))p
FA(q)338 b FO(=)606 b(del)35214 47424 y FE(0)35524 47924
y FO(\()p FG(m)p FO(\))2435 50587 y(Pra)-34 b(vilo)374
b FG(I)95 b(nit)p FO(\()p FG(m)p FO(\))375 b(je)g(jednosta)-34
b(vno)377 b(prev)-34 b(o)p 22316 49973 364 53 v(denje)375
b(u)g(m)-34 b(ultiskup)377 b(p)34 b(o)-34 b(\267)-572
b(cetnog)375 b(znanja)h(ul-)2435 52092 y(jeza)i(transformacija)i(m)-34
b(ultiskup)34 b(o)-34 b(v)-67 b(a:)526 b(ak)-34 b(o)379
b(je)f FG(m)337 b FI(2)g FG(P)27583 52274 y FB(0)28109
52092 y FO(,)383 b(gdje)c(je)f FG(P)33461 52274 y FB(0)34365
52092 y FO(p)34 b(o)-34 b(\267)-572 b(cetno)379 b(znanje)2435
53598 y(uljeza)404 b(niti,)g(tada)h FN(I)p FO(\()p FG(m)p
FO(\))338 b FI(2)e FA(p)p FG(P)16432 53780 y FB(0)16958
53598 y FA(q)h FO(=)g FG(I)19714 53780 y FB(0)20239 53598
y FO(,)404 b(p)34 b(o)-64 b(\267)-542 b(stuju)-34 b(\266)-572
b(ci)405 b(vi)-64 b(\267)-542 b(sestruk)-67 b(a)404 b(p)34
b(o)67 b(ja)-34 b(vljiv)-67 b(anja.)2435 55103 y(Nijedna)342
b(uljezo)-34 b(v)-67 b(a)340 b(nit)h(se)f(ne)g(prev)-34
b(o)34 b(di)341 b(u)g(pra)-34 b(vilo)340 b(snd)27266
54663 y FE(0)27577 55103 y FO(,)353 b(niti)341 b(u)g(pra)-34
b(vilo)340 b(rec)36973 54663 y FE(0)37282 55103 y FO(,)353
b(ali)340 b(tamo)2435 56609 y(gdje)405 b(su)f(p)34 b(otrebne)405
b(uljezu)f(transformacija)h(m)-34 b(ultiskup)34 b(o)-34
b(v)-67 b(a)371 b(\266)-572 b(ce)404 b(ih)g(k)-34 b(oristiti.)4317
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y FL(T)-116 b(eorem)464 b(5)606 b FK(Neka)428 b(su)g
FO(\()p FG(\276)-24 b(;)202 b(\276)15822 61631 y FF(])16244
62071 y FO(\))429 b FK(i)g FO(\()p FG(\276)19109 62253
y FB(1)19635 62071 y FG(;)202 b(\276)20910 61481 y FF(])20867
62418 y FB(1)21392 62071 y FO(\))430 b FK(kon\257gur)-62
b(acije)426 b(niti)j(iz)g(pr)-62 b(ostor)g(a)427 b(p)-62
b(ar)g(amet-)2435 63576 y(rizir)g(anih)473 b(niti)h FI(S)91
b FK(,)485 b(uklju)-31 b(\267)-589 b(cuju)-31 b(\266)-589
b(ci)470 b(niti)k(uljeza)e(p)-62 b(o)-31 b(\267)-589
b(cetno)-62 b(g)472 b(znanja)h FG(P)33027 63758 y FB(0)33553
63576 y FK(.)680 b(T)-93 b(ada,)483 b(za)474 b(svaki)2435
65082 y(niz)434 b(kor)-62 b(aka)16262 66587 y FO(\()p
FG(\276)-24 b(;)202 b(\276)18677 66087 y FF(])19098 66587
y FO(\))20655 65900 y FF(o)19906 66587 y FI(7\241)-202
b(!)21859 65748 y FE(\244)21859 66887 y FF(P)22456 67010
y Fk(0)22916 66887 y FF(;)p FE(S)24205 66587 y FO(\()p
FG(\276)25369 66769 y FB(1)25894 66587 y FG(;)202 b(\276)27169
65998 y FF(])27126 66934 y FB(1)27652 66587 y FO(\))p
FG(;)2435 68782 y FK(i)434 b(svaki)d FG(I)6809 68964
y FB(0)7672 68782 y FI(\265)336 b FA(p)p FG(P)10335 68964
y FB(0)10861 68782 y FA(q)434 b FK(,)f(p)-62 b(ostoji)431
b(niz)j(r)-62 b(e)g(gularnih)431 b(pr)-62 b(avila)432
b(prijelaza)12122 71444 y FA(p)p FG(P)13506 71626 y FB(0)14032
71444 y FA(q)p FG(;)202 b(S)15920 71632 y FE(S)16610
71444 y FO(\()p FG(\276)-24 b(;)202 b(\276)19025 70944
y FF(])19446 71444 y FO(\))21006 70757 y FF(r)20255 71444
y FI(\241)-203 b(!)22207 70605 y FE(\244)22207 71744
y(I)22785 71492 y FD(0)23084 71744 y FF(;)p Fg(p)p FE(S)65
b Fg(q)25313 71444 y FG(S)26056 71632 y FE(S)26747 71444
y FO(\()p FG(\276)27911 71626 y FB(1)28437 71444 y FG(;)202
b(\276)29712 70855 y FF(])29669 71792 y FB(1)30194 71444
y FO(\))p FG(;)g(I)31737 71626 y FB(0)32262 71444 y FG(:)21755
74956 y FO(65)p eop end end
%%Page: 66 66
TeXDict begin HPSdict begin 66 65 bop 9631 7181 a FO(Uo)-34
b(\267)-572 b(cimo,)653 b(o)-34 b(vdje)604 b(niz)g(k)-34
b(orak)-67 b(a)603 b(ne)g(mora)h(p)34 b(o)-34 b(\267)-572
b(ceti)604 b(iz)f(prazne)g(k)-34 b(on\257guracije,)654
b(za)7749 8687 y(razliku)523 b(o)34 b(d)524 b(prijev)-34
b(o)34 b(da)524 b(u)h(drugom)g(smjeru)f({)h(to)f(je)g(stoga)461
b(\267)-542 b(sto)525 b(stanja)g(ne)g(pam)-34 b(te,)7749
10192 y(zna)67 b(ju)369 b(samo)g(za)f(sada)-64 b(\267)-542
b(snji)369 b(tren)-34 b(utak.)528 b(Naprotiv,)375 b(k)-34
b(on\257guracije)369 b(nose)g(informacije)f(o)7749 11698
y(tome)404 b(k)-67 b(ak)-34 b(o)404 b(se)g(nit,)g(o)34
b(dnosno)405 b(k)-34 b(om)g(unik)-67 b(acija)404 b(u)h(protok)-34
b(olu,)404 b(razvijala.)27068 74956 y(66)p eop end end
%%Page: 67 67
TeXDict begin HPSdict begin 67 66 bop 2435 15745 a FJ(P)-72
b(ogla)g(vlje)864 b(6)2435 21541 y FM(Strune)2435 27735
y FO(Mo)34 b(del)407 b(struna)h(\()p FK(c)-62 b(or)g(ds)99
b FO(\))407 b(je)h(p)34 b(oku)-64 b(\267)-542 b(sa)67
b(j)408 b(da)g(se)f(ob)67 b(jedine)408 b(i)f(p)34 b(ob)g(olj)-64
b(\267)-542 b(sa)67 b(ju)409 b(dv)-67 b(a)407 b(pretho)34
b(dno)2435 29241 y(opisana)469 b(mo)34 b(dela.)728 b(Role)467
b(protok)-34 b(ola)468 b(se)g(opisuju)g(nitima,)484 b(i)467
b(osno)-34 b(vna)469 b(ideja)e(sti)-34 b(\267)-572 b(ze)467
b(iz)2435 30746 y(mo)34 b(dela)551 b(niti,)588 b(no)551
b(metafora)h(niti)f(je)g(ob)34 b(oga)-34 b(\266)-572
b(cena)552 b(i)e(p)34 b(o)67 b(ja)-64 b(\267)-542 b(snjena.)982
b(Umjesto)552 b(da)f(su)2435 32252 y(parametrizirane,)485
b(niti)470 b(su)g(sada)h(snab)34 b(djev)-34 b(ene)470
b(v)-67 b(arijablama,)486 b(i)469 b(adekv)-67 b(atnim)470
b(meh-)2435 33757 y(anizmom)455 b(za)e(supstituciju)k(v)-67
b(arijabli.)687 b(P)-34 b(osto)67 b(je)456 b(k)-34 b(onstrukti)455
b(za)f(generiranje)f(no)-34 b(vih)2435 35263 y(vrijednosti)405
b(i)e(dekrip)34 b(ciju,)404 b(k)-34 b(o)67 b(ji)404 b(v)-34
b(e)g(\267)-572 b(zu)404 b(v)-67 b(arijable.)2435 36768
y(Mo)34 b(del)404 b(je)g(predsta)-34 b(vljen)405 b(u)g([DMP01)o(].)4317
40040 y(Protok)-34 b(oli)481 b(se)h(sp)34 b(eci\257cira)67
b(ju)481 b(pro)34 b(cesima,)466 b(\267)-572 b(cija)481
b(je)h(op)34 b(erativna)481 b(seman)-34 b(tik)-67 b(a)482
b(dana)2435 41546 y(k)-67 b(ao)497 b(v)-67 b(arijan)-34
b(ta)497 b(ra)-34 b(\267)-572 b(cuna)498 b(pro)34 b(cesa)496
b(i)h(oslanja)g(se)g(na)h FG(\274)43 b FO(-ra)-34 b(\267)-572
b(cun)497 b(\([MPW92]\),)520 b(a)498 b(blisk)-67 b(a)2435
43051 y(je)654 b(i)f(spi-ra)-34 b(\267)-572 b(cun)-34
b(u)654 b(\([A)-34 b(G97)q(]\).)1287 b(Usp)34 b(ore)p
21392 42438 364 53 v(den)653 b(sa)h FG(\274)43 b FO(-ra)-34
b(\267)-572 b(cunom,)716 b(formalizam)653 b(se)620 b(\267)-572
b(cini)2435 44557 y(oslabljenim,)447 b(s)438 b(obzirom)g(da)h(se)f(k)
-34 b(om)g(unik)-67 b(acijski)438 b(k)-67 b(anali)437
b(ne)h(mo)34 b(delira)67 b(ju)439 b(eksplicit-)2435 46062
y(no,)336 b(dakle,)f(nema)319 b(brige)g(ok)-34 b(o)319
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b(\267)-542 b(sta)-34 b(v)-67 b(anja.)512 b(Dok)318 b
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%%Page: 68 68
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%%Page: 69 69
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b(dre)p 9819 54053 364 53 v(den)281 b(je)g(zagradama,)306
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b(se)g(de\257nira)67 b(ju)320 b(induktivno.)511 b(Nek)-67
b(a)318 b(je)g FG(f)130 b(v)43 b FO(\()p FG(S)70 b FO(\))320
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b(v)-67 b(arijabli)321 b(niti)i FG(S)70 b FO(,)338 b(a)322
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b(niti)f FG(S)70 b FO(.)539 b(T)-101 b(ada)405 b(je)f
FG(f)130 b(v)43 b FO(\()p FG(S)70 b FO(\):)4253 64566
y FI(\262)607 b FG(f)130 b(v)43 b FO(\()p FG(t)p FO(\),)405
b(gdje)f(je)h FG(t)e FO(term,)h(je)g(skup)h(svih)f(v)-67
b(arijabli)403 b(iz)g FG(t)4253 67016 y FI(\262)607 b
FG(f)130 b(v)43 b FO(\()p FI(h)p FG(t)p FI(i)p FG(S)70
b FO(\))339 b(=)d FG(f)130 b(v)43 b FO(\()p FG(t)p FO(\))271
b FI([)e FG(f)130 b(v)43 b FO(\()p FG(S)70 b FO(\))4253
69466 y FI(\262)607 b FG(f)130 b(v)43 b FO(\(\()p FG(x)p
FO(\))p FG(S)70 b FO(\))339 b(=)d FG(f)130 b(v)43 b FO(\()p
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b FG(f)130 b(v)43 b FO(\(\()p FG(\272)77 b(x)p FO(\))p
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b FO(\))p FI(nf)p FG(x)p FI(g)21755 74956 y FO(69)p eop
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%%Page: 70 70
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FO(\()p FG(t)p FO(\))271 b FI([)e FO(\()p FG(f)130 b(v)43
b FO(\()p FG(S)70 b FO(\))p FI(nf)p FG(x)p FI(g)p FO(\))9631
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b(v)43 b FO(\()p FG(S)70 b FO(\))406 b(su)e(iz)g FG(bv)43
b FO(\()p FG(S)70 b FO(\).)9631 11168 y(Prije)415 b(nego)351
b(\267)-542 b(sto)417 b(ob)67 b(jasnimo)417 b(k)-67 b(ak)-34
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b FI(,)25350 30957 y Fi(\275)26812 31911 y FG(f)130 b(v)43
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7749 43340 y(lencije)432 b(niti)h(skup)-62 b(a)431 b
FI(S)525 b FK(za)433 b(r)-62 b(elaciju)431 b FI(\274)p
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b(a)403 b(i)g(uljezo)-34 b(vim)404 b(strunama.)9631 69501
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FO(su)i(sljede)-34 b(\266)-572 b(ca:)13320 71916 y Fy([\()p
Fw(x)p Fy(\))p Fw(S)64 b Fy(])248 b Ft(\255)e Fy([)p
Ft(h)p Fw(t)p Ft(i)p Fw(T)154 b Fy(])247 b Ft(\255)f
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Fw(C)18 b(;)2527 b(f)119 b(v)40 b Fy(\()p Fw(t)p Fy(\))308
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%%Page: 71 71
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b(esti)385 b(o)34 b(dgo)-34 b(v)-67 b(ara)67 b(ju)-34
b(\266)-572 b(ci)386 b(priv)-67 b(atni)386 b(klju)-34
b(\267)-572 b(c)385 b(jer)h(nema)f(takv)-34 b(og)386
b(k)-34 b(on-)2435 68905 y(struktora)389 b(u)f(jeziku.)533
b(Ov)-67 b(a)67 b(j)388 b(apstraktni)h(mo)34 b(del)388
b(je)g(predvi)p 29996 68292 V(den)g(za)g(mo)34 b(deliranje)388
b(pro-)2435 70411 y(tok)-34 b(ola)405 b(k)-34 b(o)67
b(ji)404 b(ne)g(izmjenjuju)i(priv)-67 b(atne)404 b(klju)-34
b(\267)-572 b(cev)-34 b(e)403 b(me)p 27245 69797 V(du)i(sudionicima.)
21755 74956 y(71)p eop end end
%%Page: 72 72
TeXDict begin HPSdict begin 72 71 bop 9631 7181 a FO(Sada)405
b(mo)-34 b(\267)-572 b(zemo)403 b(de\257nirati)i(Dolev-Y)-101
b(ao)403 b(protok)-34 b(ol)405 b(k)-67 b(ao)403 b(prostor)i(struna:)
22376 9447 y FG(D)34 b(Y)605 b FO(=)336 b FI(f)p FG(I)95
b(nit;)202 b(R)9 b(esp)p FI(g)p FG(;)7749 11713 y FO(pri)299
b(tom)h(iniciramo)e(p)34 b(o)299 b(v)-34 b(olji)299 b(mnogo)h(puta)h
(neku)e(rolu)g(instancira)67 b(ju)-34 b(\266)-572 b(ci)300
b(o)34 b(dgo)-34 b(v)-67 b(ara)67 b(ju)-34 b(\266)-572
b(cu)7749 13218 y(nit)374 b(s)g(imenima)g(agenata.)529
b(Nak)-34 b(on)375 b(toga)f(se)g(role)f(k)-34 b(omp)34
b(onira)67 b(ju)375 b(prema)f(danim)h(reak-)7749 14724
y(cijama)404 b(za)g(strune,)g(na)h(primjer:)9040 18106
y Fw(I)87 b(nit)p Fy(\()p Fw(A;)184 b(B)56 b Fy(\))248
b Ft(\255)d Fw(R)9 b(esp)p Fy(\()p Fw(B)56 b Fy(\))307
b Ff(BB)h Fy([\()p Fw(\272)70 b(x)p Fy(\))p Ft(hff)p
Fw(x)p Ft(g)27163 18272 y Fv(B)27928 18106 y Fw(;)184
b(A)p Ft(g)29802 18272 y Fv(B)30565 18106 y Ft(i)p Fy(\()p
Fw(u)p Fy(\)\()p Fw(u=)p Ft(f)p Fw(y)40 b(;)184 b(B)56
b Ft(g)p 37182 17800 722 38 v 337 x Fv(A)37906 18106
y Fy(\)\()p Fw(y)40 b(=)p Ft(f)p Fw(x)p Ft(g)p 41641
17800 V 337 x Fv(A)42363 18106 y Fy(\)])43100 18272 y
Fv(A)44007 18106 y Ft(\255)22147 19767 y(\255)246 b Fy([\()p
Fw(v)40 b Fy(\)\()p Fw(v)g(=)p Ft(f)p Fw(y)g(;)184 b(a)p
Ft(g)p 29323 19461 762 38 v 336 x Fv(B)30087 19767 y
Fy(\)\()p Fw(y)40 b(=)p Ft(f)p Fw(x)p Ft(g)p 33822 19461
V 336 x Fv(B)34586 19767 y Fy(\))p Ft(hff)p Fw(x)p Ft(g)37738
19933 y Fv(a)38275 19767 y Fw(;)184 b(B)56 b Ft(g)40215
19933 y Fv(a)40751 19767 y Ft(i)p Fy(])41488 19933 y
Fv(B)19994 21427 y Ff(BB)308 b Fy([)p Ft(hff)p Fw(N)121
b Ft(g)25430 21593 y Fv(B)26194 21427 y Fw(;)184 b(A)p
Ft(g)28068 21593 y Fv(B)28832 21427 y Ft(i)p Fy(\()p
Fw(u)p Fy(\)\()p Fw(u=)p Ft(f)p Fw(y)40 b(;)184 b(B)56
b Ft(g)p 35449 21121 722 38 v 337 x Fv(A)36172 21427
y Fy(\)\()p Fw(y)40 b(=)p Ft(f)p Fw(N)121 b Ft(g)p 40284
21121 V 337 x Fv(A)41007 21427 y Fy(\)])41744 21593 y
Fv(A)42651 21427 y Ft(\255)22147 23088 y(\255)246 b Fy([\()p
Fw(v)40 b Fy(\)\()p Fw(v)g(=)p Ft(f)p Fw(y)g(;)184 b(a)p
Ft(g)p 29323 22782 762 38 v 336 x Fv(B)30087 23088 y
Fy(\)\()p Fw(y)40 b(=)p Ft(f)p Fw(x)p Ft(g)p 33822 22782
V 336 x Fv(B)34586 23088 y Fy(\))p Ft(hff)p Fw(x)p Ft(g)37738
23254 y Fv(a)38275 23088 y Fw(;)184 b(B)56 b Ft(g)40215
23254 y Fv(a)40751 23088 y Ft(i)p Fy(])41488 23254 y
Fv(B)19994 24748 y Ff(BB)308 b Fy([\()p Fw(u)p Fy(\)\()p
Fw(u=)p Ft(f)p Fw(y)40 b(;)184 b(B)56 b Ft(g)p 28518
24442 722 38 v 337 x Fv(A)29241 24748 y Fy(\)\()p Fw(y)40
b(=)p Ft(f)p Fw(N)121 b Ft(g)p 33353 24442 V 337 x Fv(A)34076
24748 y Fy(\)])34813 24914 y Fv(A)35720 24748 y Ft(\255)22147
26409 y(\255)246 b Fy([\()p Ft(ff)p Fw(N)121 b Ft(g)26660
26575 y Fv(B)27424 26409 y Fw(;)184 b(A)p Ft(g)29298
26575 y Fv(B)30062 26409 y Fw(=)p Ft(f)p Fw(y)40 b(;)184
b(a)p Ft(g)p 33380 26103 762 38 v 336 x Fv(B)34144 26409
y Fy(\)\()p Fw(y)40 b(=)p Ft(f)p Fw(x)p Ft(g)p 37879
26103 V 336 x Fv(B)38642 26409 y Fy(\))p Ft(hff)p Fw(x)p
Ft(g)41794 26575 y Fv(a)42332 26409 y Fw(;)184 b(B)56
b Ft(g)44272 26575 y Fv(a)44808 26409 y Ft(i)p Fy(])45545
26575 y Fv(B)19994 28069 y Ff(BB)308 b Fy([\()p Fw(u)p
Fy(\)\()p Fw(u=)p Ft(f)p Fw(y)40 b(;)184 b(B)56 b Ft(g)p
28518 27763 722 38 v 336 x Fv(A)29241 28069 y Fy(\)\()p
Fw(y)40 b(=)p Ft(f)p Fw(N)121 b Ft(g)p 33353 27763 V
336 x Fv(A)34076 28069 y Fy(\)])34813 28235 y Fv(A)35720
28069 y Ft(\255)22147 29729 y(\255)246 b Fy([\()p Ft(f)p
Fw(N)121 b Ft(g)26107 29895 y Fv(B)26871 29729 y Fw(=)p
Ft(f)p Fw(x)p Ft(g)p 29163 29423 762 38 v 337 x Fv(B)29926
29729 y Fy(\))p Ft(hff)p Fw(x)p Ft(g)33078 29895 y Fv(A)33801
29729 y Fw(;)184 b(B)56 b Ft(g)35741 29895 y Fv(A)36463
29729 y Ft(i)p Fy(])37200 29895 y Fv(B)19994 31390 y
Ff(BB)308 b Fy([\()p Fw(u)p Fy(\)\()p Fw(u=)p Ft(f)p
Fw(y)40 b(;)184 b(B)56 b Ft(g)p 28518 31084 722 38 v
336 x Fv(A)29241 31390 y Fy(\)\()p Fw(y)40 b(=)p Ft(f)p
Fw(N)121 b Ft(g)p 33353 31084 V 336 x Fv(A)34076 31390
y Fy(\)])34813 31556 y Fv(A)35966 31390 y Ft(\255)246
b Fy([)p Ft(hff)p Fw(N)121 b Ft(g)40479 31556 y Fv(A)41202
31390 y Fw(;)184 b(B)56 b Ft(g)43142 31556 y Fv(A)43864
31390 y Ft(i)p Fy(])44601 31556 y Fv(B)19994 33050 y
Ff(BB)308 b Fy([\()p Ft(ff)p Fw(N)121 b Ft(g)25430 33216
y Fv(A)26153 33050 y Fw(;)184 b(B)56 b Ft(g)28093 33216
y Fv(A)28815 33050 y Fw(=)p Ft(f)p Fw(y)40 b(;)184 b(B)56
b Ft(g)p 32444 32744 V 337 x Fv(A)33166 33050 y Fy(\)\()p
Fw(y)40 b(=)p Ft(f)p Fw(N)121 b Ft(g)p 37278 32744 V
337 x Fv(A)38001 33050 y Fy(\)])38738 33216 y Fv(A)39891
33050 y Ft(\255)246 b Fy([)308 b(])41920 33216 y Fv(B)19994
34711 y Ff(BB)g Fy([\()p Ft(f)p Fw(N)121 b Ft(g)24877
34877 y Fv(A)25600 34711 y Fw(=)p Ft(f)p Fw(N)g Ft(g)p
28269 34405 V 336 x Fv(A)28992 34711 y Fy(\)])29729 34877
y Fv(A)30881 34711 y Ft(\255)246 b Fy([)308 b(])32910
34877 y Fv(B)19994 36371 y Ff(BB)g Fy([)g(])22946 36537
y Fv(A)24098 36371 y Ft(\255)246 b Fy([)308 b(])26127
36537 y Fv(B)9631 40108 y FO(Ov)-67 b(a)67 b(j)476 b(niz)h(reak)-34
b(cija)477 b(da)67 b(je)478 b(k)-34 b(orektn)g(u)477
b(rundu)i(Dolev-Y)-101 b(ao)476 b(protok)-34 b(ola.)758
b(Nara)-34 b(vno,)7749 41613 y(nas)291 b(\266)-572 b(ce)323
b(zanimati)261 b(\267)-542 b(sto)325 b(mo)-34 b(\267)-572
b(ze)324 b(do)-34 b(v)g(esti)325 b(do)f(lo)-64 b(\267)-542
b(sih)325 b(rundi,)340 b(stoga)325 b({)g(moramo)f(sp)34
b(eci\257cirati)7749 43119 y(uljeza.)7749 46249 y FL(Uljezo)-39
b(v)g(e)464 b(ak)-39 b(cije)7749 48537 y FO(Uljez)303
b(mo)-34 b(\267)-572 b(ze)302 b(izv)-34 b(esti)303 b(sv)-67
b(aku)303 b(ak)-34 b(ciju)303 b(k)-34 b(o)67 b(ju)305
b(mo)-34 b(\267)-572 b(ze)303 b(i)g(p)34 b(o)-64 b(\267)-542
b(steni)303 b(sudionik)h(protok)-34 b(ola,)324 b(dakle)7749
50042 y(sv)-67 b(aku)508 b(ak)-34 b(ciju)510 b(struna.)854
b(Drugim)509 b(rije)-34 b(\267)-572 b(cima,)534 b(uljez)509
b(mo)-34 b(\267)-572 b(ze)509 b(instancirati)g(proizv)-34
b(oljn)g(u)7749 51548 y(strun)g(u,)520 b(doklego)34 b(d)496
b(su)g(dekrip)34 b(cije)495 b(k)-34 b(o)67 b(je)496 b(izv)-34
b(o)34 b(di)495 b(samo)h(one)g(za)g(k)-34 b(o)67 b(je)496
b(ima)g(p)34 b(otrebni)7749 53053 y(klju)-34 b(\267)-572
b(c.)522 b(Rola)357 b(uljeza)f(k)-34 b(o)67 b(ji)357
b(p)34 b(osjeduje)357 b(priv)-67 b(atne)356 b(klju)-34
b(\267)-572 b(cev)-34 b(e)p 34342 52080 1117 49 v 356
w FG(K)35458 53235 y FB(1)35984 53053 y FG(;)p 36523
52080 V 202 w(K)37639 53235 y FB(2)38165 53053 y FG(;)202
b(:)g(:)g(:)e(;)p 40858 52080 V 202 w(K)41974 53235 y
FF(n)42957 53053 y FO(je)356 b(struna)7749 54559 y FG(I)385
b FO(indeksirana)290 b(sa)g FG(K)17397 54741 y FB(1)17923
54559 y FG(;)202 b(K)19491 54741 y FB(2)20017 54559 y
FG(;)g(:)g(:)g(:)f(;)h(K)23740 54741 y FF(n)24366 54559
y FO(,)313 b(gdje)290 b(se)g(samo)g(klju)-34 b(\267)-572
b(cevi)p 36155 53585 V 289 w FG(K)37271 54741 y FB(1)37797
54559 y FG(;)p 38336 53585 V 202 w(K)39452 54741 y FB(1)39978
54559 y FG(;)202 b(:)g(:)g(:)f(;)p 42672 53585 V 202
w(K)43787 54741 y FF(n)44704 54559 y FO(mogu)7749 56064
y(p)34 b(o)67 b(ja)-34 b(viti)405 b(u)f(uzorcima)g(dekrip)34
b(cije.)7749 57570 y(Radi)404 b(se)g(o)g(uobi)-34 b(\267)-572
b(ca)67 b(jenom)406 b(Dolev-Y)-101 b(ao)403 b(napada)-34
b(\267)-572 b(cu.)9631 60581 y(Za)348 b(sv)-67 b(aki)348
b(protok)-34 b(ol)350 b(moramo)f(opisati)g(pripadni)h(prostor)f(struna)
h FG(C)87 b FO(.)521 b(Pretho)34 b(dno)7749 62086 y(o)g(dre)p
10336 61473 364 53 v(dujemo)404 b FK(inicijalnu)432 b(kon\257gur)-62
b(aciju)495 b FO(imen)-34 b(uju)g(\266)-572 b(ci:)9567
64207 y FI(\262)606 b FO(skup)405 b(agenata)g FG(P)18938
64395 y FF(C)20063 64207 y FO(=)336 b FI(f)p FG(P)22726
64389 y FB(1)23252 64207 y FG(;)202 b(P)24569 64389 y
FB(2)25095 64207 y FG(;)g(:)g(:)g(:)f(;)h(P)28567 64404
y FF(k)29136 64207 y FI(g)404 b FO(k)-34 b(o)67 b(ji)405
b(mogu)f(p)34 b(ersoni\257cirati)404 b(role;)9567 66556
y FI(\262)606 b FG(H)98 b(O)34 b(N)132 b(E)70 b(S)g(T)168
b FO(\()p FG(C)87 b FO(\))337 b(=)g FI(f)p FG(P)21500
66738 y FB(1)22026 66556 y FG(;)202 b(P)23343 66738 y
FB(2)23869 66556 y FG(;)g(:)g(:)g(:)e(P)26801 66753 y
FF(l)27148 66556 y FI(g)337 b(\265)g FG(P)30149 66744
y FF(C)30937 66556 y FO(,)404 b(skup)h(p)34 b(o)-64 b(\267)-542
b(stenih)405 b(agenata;)9567 68905 y FI(\262)606 b FO(uljezo)-34
b(vu)270 b(rolu)f FG(I)18285 69093 y FF(C)19410 68905
y FO(=)337 b([)p FG(:)202 b(:)g(:)n FO(])22777 69093
y FF(P)23374 69249 y FC(l)p Fk(+1)24723 69093 y FF(;:::)q(;P)26626
69249 y FC(k)27190 68905 y FO(,)296 b(gdje)270 b(su)f
FG(P)32479 69102 y FF(l)11 b FB(+1)34029 68905 y FG(;)202
b(:)g(:)g(:)e(;)i(P)37500 69102 y FF(k)38339 68905 y
FO(klju)-34 b(\267)-572 b(cevi)268 b(za)h(dekrip-)10779
70411 y(ciju)498 b(p)34 b(oznati)499 b(uljezu.)821 b(Jedan)499
b(o)34 b(d)498 b(klju)-34 b(\267)-572 b(cev)-67 b(a)498
b(je)g(uljezo)-34 b(v)498 b(klju)-34 b(\267)-572 b(c,)522
b(ili)497 b(-)h(uljezom)10779 71916 y(mo)-34 b(\267)-572
b(zemo)404 b(smatrati)g(ob)67 b(jedinjene)406 b(sv)-34
b(e)404 b(nep)34 b(o)-64 b(\267)-542 b(stene)405 b(agen)-34
b(te)404 b(prostora)h FG(C)87 b FO(.)27068 74956 y(72)p
eop end end
%%Page: 73 73
TeXDict begin HPSdict begin 73 72 bop 2435 7181 a FO(Nak)-34
b(on)405 b(inicijalne)f(k)-34 b(on\257guracije)404 b(de\257niramo)h
(prostor)f(struna)i FG(C)87 b FO(:)7400 9995 y FG(C)424
b FO(=)p FG(I)95 b(nit)p FO(\()p FG(X)13320 10177 y FB(1)13845
9995 y FG(;)202 b(Y)15088 10177 y FB(1)15613 9995 y FO(\))472
b FI(\255)269 b FG(I)95 b(nit)p FO(\()p FG(X)21455 10177
y FB(2)21980 9995 y FG(;)202 b(Y)23223 10177 y FB(2)23748
9995 y FO(\))472 b FI(\255)269 b FG(:)202 b(:)g(:)471
b FI(\255)269 b FG(I)95 b(nit)p FO(\()p FG(X)32688 10177
y FF(m)33575 9995 y FG(;)202 b(Y)34818 10177 y FF(m)35705
9995 y FO(\))g FI(\255)9902 11832 y(\255)269 b FG(R)9
b(esp)p FO(\()p FG(Z)15083 12014 y FB(1)15611 11832 y
FO(\))472 b FI(\255)269 b FG(I)95 b(nit)p FO(\()p FG(Z)21276
12014 y FB(2)21801 11832 y FO(\))472 b FI(\255)269 b
FG(:)202 b(:)g(:)471 b FI(\255)269 b FG(I)95 b(nit)p
FO(\()p FG(Z)30564 12014 y FF(n)31190 11832 y FO(\))202
b FI(\255)9902 13670 y(\255)269 b FG(I)11647 13858 y
FF(C)12435 13670 y FO(\()p FG(P)13684 13867 y FF(l)11
b FB(+1)15234 13670 y FG(;)202 b(:)g(:)g(:)f(;)h(P)18706
13867 y FF(k)19275 13670 y FO(\))2435 16483 y(gdje)341
b(su)f FG(X)7459 16665 y FF(i)8174 16483 y FO(i)g FG(Z)9678
16665 y FF(j)10505 16483 y FO(u)g FG(H)98 b(O)34 b(N)132
b(E)70 b(S)g(T)168 b FO(\()p FG(C)87 b FO(\).)517 b FG(H)98
b(O)34 b(N)132 b(E)70 b(S)g(T)168 b FO(\()p FG(C)87 b
FO(\))341 b(je)e(skup)i(imena)e(svih)h(agenata)2435 17988
y(k)-34 b(o)67 b(ji)391 b(p)34 b(o)-64 b(\267)-542 b(stuju)392
b(protok)-34 b(ol,)393 b(preuzima)67 b(ju)-34 b(\266)-572
b(ci)391 b(uloge)f(inicijatora)g(ili)f(o)34 b(dzivnik)-67
b(a.)533 b(Sv)-67 b(ak)g(ak)-34 b(o,)2435 19494 y(p)34
b(o)-64 b(\267)-542 b(steni)369 b(sudionik)f(ne)g(mo)-34
b(\267)-572 b(ze)367 b(znati)h(da)h(li)e(zap)34 b(o)-34
b(\267)-572 b(cinje)367 b(sesiju)i(s)f(p)34 b(o)-64 b(\267)-542
b(stenim)368 b(sudionik)-34 b(om)2435 20999 y(ili)431
b(nep)34 b(o)-64 b(\267)-542 b(stenim,)405 b(\267)-572
b(ciji)430 b(je)i(klju)-34 b(\267)-572 b(c)431 b(k)-34
b(ompromitiran.)621 b(Kom)-34 b(unik)-67 b(acija)432
b(s)f(agen)-34 b(tom)399 b(\267)-572 b(ciji)431 b(je)2435
22505 y(klju)-34 b(\267)-572 b(c)404 b(za)g(dekrip)34
b(ciju)404 b(p)34 b(oznat)404 b(uljezu)h(zna)-34 b(\267)-572
b(ci)403 b(k)-34 b(om)g(unik)-67 b(aciju)405 b(s)f(uljezom.)4317
25369 y(Kao)429 b(primjer)g(inicijalne)g(k)-34 b(on\257guracije)430
b(k)-34 b(o)67 b(ja)430 b(v)-34 b(o)34 b(di)429 b(do)h(lo)-64
b(\267)-542 b(se)429 b(runde,)436 b(opi)-64 b(\267)-542
b(simo)429 b(se)2435 26697 y(jo)-64 b(\267)-542 b(s)405
b(jednom)g(napada)g(na)g(Dolev-Y)-101 b(ao)403 b(protok)-34
b(ol,)405 b(te)f(imamo:)8031 29192 y Fw(P)8742 29358
y Fv(C)10901 29192 y Fy(=)1414 b Ft(f)p Fw(A;)184 b(B)56
b(;)184 b(E)64 b Ft(g)2435 30853 y Fw(H)90 b(O)31 b(N)121
b(E)64 b(S)g(T)154 b Fy(\()p Fw(C)79 b Fy(\))1416 b(=)e
Ft(f)p Fw(A;)184 b(B)56 b Ft(g)8255 32513 y Fw(I)8742
32679 y Fv(C)10901 32513 y Fy(=)1414 b(\()p Fw(a;)184
b(b;)g(e)p Fy(\)[\()p Fw(x)p Fy(\))p Ft(h)p Fw(x)p Ft(ihf)p
Fw(x;)g(e)p Ft(g)23061 32679 y Fv(b)23513 32513 y Ft(i)p
Fy(\()p Fw(u)p Fy(\)\()p Fw(u=)p Ft(f)p Fw(v)40 b(;)184
b(b)p Ft(g)p 29703 32233 476 38 v 166 x Fv(e)30182 32513
y Fy(\)\()p Fw(v)40 b(=)p Ft(f)p Fw(y)g(;)184 b(a)p Ft(g)p
34937 32233 V 166 x Fv(e)35414 32513 y Fy(\))p Ft(hf)p
Fw(y)40 b(;)184 b(e)p Ft(g)38969 32679 y Fv(b)39417 32513
y Ft(i)13053 34174 y Fy(\()p Fw(w)30 b Fy(\)\()p Fw(w)g(=)p
Ft(f)p Fw(z)49 b(;)184 b(b)p Ft(g)p 19176 33893 V 166
x Fv(e)19655 34174 y Fy(\)\()p Fw(z)49 b(=)p Ft(f)p Fw(s)p
Ft(g)p 23257 33893 V 166 x Fv(e)23734 34174 y Fy(\)])24471
34340 y Fv(E)8616 35834 y Fw(C)1494 b Fy(=)1414 b Fw(I)87
b(nit)p Fy(\()p Fw(A;)184 b(B)56 b Fy(\))432 b Ft(\255)246
b Fw(R)9 b(esp)p Fy(\()p Fw(B)56 b Fy(\))430 b Ft(\255)246
b Fw(R)9 b(esp)p Fy(\()p Fw(B)56 b Fy(\))430 b Ft(\255)246
b Fw(R)9 b(esp)p Fy(\()p Fw(B)56 b Fy(\))429 b Ft(\255)246
b Fw(I)37499 36000 y Fv(C)38244 35834 y Fy(\()p Fw(A;)184
b(B)56 b(;)184 b(E)64 b Fy(\))4317 39865 y FO(P)-34 b(o)g(\267)-572
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Fy(\))p Ft(hf)p Fw(y)40 b(;)184 b(E)64 b Ft(g)27275 28933
y Fv(B)28039 28767 y Ft(i)p Fy(\()p Fw(w)30 b Fy(\))184
b Fw(:)g(:)g(:)5 b Fy(])31936 28933 y Fv(E)8927 30427
y Ff(BB)245 b Fy([)308 b(])11816 30593 y Fv(A)12968 30427
y Ft(\255)246 b Fy([)308 b(])14997 30593 y Fv(B)16190
30427 y Ft(\255)246 b Fy([)308 b(])18219 30593 y Fv(B)19412
30427 y Ft(\255)246 b Fy([\()p Ft(fff)p Fw(N)121 b Ft(g)24478
30593 y Fv(B)25243 30427 y Fw(;)184 b(A)p Ft(g)27117
30593 y Fv(E)27866 30427 y Fw(;)g(B)56 b Ft(g)29806 30593
y Fv(E)30555 30427 y Fw(=)p Ft(f)p Fw(y)40 b(;)184 b(A)p
Ft(g)p 34118 30121 762 38 v 337 x Fv(B)34882 30427 y
Fy(\))g Fw(:)g(:)g(:)s Fy(])37095 30593 y Fv(B)38042
30427 y Ft(\255)11140 32088 y(\255)246 b Fy([)p Ft(hff)p
Fw(N)121 b Ft(g)15653 32254 y Fv(B)16418 32088 y Fw(;)184
b(E)64 b Ft(g)18343 32254 y Fv(B)19106 32088 y Ft(i)p
Fy(\()p Fw(w)30 b Fy(\)\()p Fw(w)g(=)p Ft(f)p Fw(z)49
b(;)184 b(B)56 b Ft(g)p 26080 31782 748 38 v 336 x Fv(E)26832
32088 y Fy(\))184 b Fw(:)g(:)g(:)s Fy(])29045 32254 y
Fv(E)8927 33748 y Ff(BB)245 b Fy([)308 b(])11816 33914
y Fv(A)12968 33748 y Ft(\255)246 b Fy([)308 b(])14997
33914 y Fv(B)16190 33748 y Ft(\255)246 b Fy([)308 b(])18219
33914 y Fv(B)19412 33748 y Ft(\255)246 b Fy([\()p Ft(ff)p
Fw(N)121 b Ft(g)23925 33914 y Fv(B)24689 33748 y Fw(;)184
b(E)64 b Ft(g)26614 33914 y Fv(B)27378 33748 y Fw(=)p
Ft(f)p Fw(y)40 b(;)184 b(a)p Ft(g)p 30696 33442 762 38
v 337 x Fv(B)31460 33748 y Fy(\)\()p Fw(y)40 b(=)p Ft(f)p
Fw(x)p Ft(g)p 35195 33442 V 337 x Fv(B)35958 33748 y
Fy(\))184 b Fw(:)g(:)g(:)t Fy(])38172 33914 y Fv(B)39118
33748 y Ft(\255)11140 35409 y(\255)246 b Fy([\()p Fw(w)30
b Fy(\)\()p Fw(w)g(=)p Ft(f)p Fw(z)49 b(;)184 b(B)56
b Ft(g)p 19098 35103 748 38 v 336 x Fv(E)19850 35409
y Fy(\)\()p Fw(z)49 b(=)p Ft(f)p Fw(s)p Ft(g)p 23452
35103 V 336 x Fv(E)24201 35409 y Fy(\)])24938 35575 y
Fv(E)8927 37069 y Ff(BB)245 b Fy([)308 b(])11816 37235
y Fv(A)12968 37069 y Ft(\255)246 b Fy([)308 b(])14997
37235 y Fv(B)16190 37069 y Ft(\255)246 b Fy([)308 b(])18219
37235 y Fv(B)19412 37069 y Ft(\255)246 b Fy([\()p Ft(f)p
Fw(N)121 b Ft(g)23372 37235 y Fv(B)24136 37069 y Fw(=)p
Ft(f)p Fw(x)p Ft(g)p 26428 36763 762 38 v 337 x Fv(B)27191
37069 y Fy(\))p Ft(hff)p Fw(x)p Ft(g)30343 37235 y Fv(E)31093
37069 y Fw(;)184 b(B)56 b Ft(g)33033 37235 y Fv(E)33781
37069 y Ft(i)p Fy(])34518 37235 y Fv(B)35466 37069 y
Ft(\255)11140 38730 y(\255)246 b Fy([\()p Fw(w)30 b Fy(\)\()p
Fw(w)g(=)p Ft(f)p Fw(z)49 b(;)184 b(B)56 b Ft(g)p 19098
38424 748 38 v 336 x Fv(E)19850 38730 y Fy(\)\()p Fw(z)49
b(=)p Ft(f)p Fw(s)p Ft(g)p 23452 38424 V 336 x Fv(E)24201
38730 y Fy(\)])24938 38896 y Fv(E)8927 40390 y Ff(BB)245
b Fy([)308 b(])11816 40556 y Fv(A)12968 40390 y Ft(\255)246
b Fy([)308 b(])14997 40556 y Fv(B)16190 40390 y Ft(\255)246
b Fy([)308 b(])18219 40556 y Fv(B)19412 40390 y Ft(\255)246
b Fy([)p Ft(hff)p Fw(N)121 b Ft(g)23925 40556 y Fv(E)24675
40390 y Fw(;)184 b(B)56 b Ft(g)26615 40556 y Fv(E)27364
40390 y Ft(i)p Fy(])28101 40556 y Fv(B)29048 40390 y
Ft(\255)11140 42051 y(\255)246 b Fy([\()p Fw(w)30 b Fy(\)\()p
Fw(w)g(=)p Ft(f)p Fw(z)49 b(;)184 b(B)56 b Ft(g)p 19098
41744 V 336 x Fv(E)19850 42051 y Fy(\)\()p Fw(z)49 b(=)p
Ft(f)p Fw(s)p Ft(g)p 23452 41744 V 336 x Fv(E)24201 42051
y Fy(\)])24938 42217 y Fv(E)8927 43711 y Ff(BB)245 b
Fy([)308 b(])11816 43877 y Fv(A)12968 43711 y Ft(\255)246
b Fy([)308 b(])14997 43877 y Fv(B)16190 43711 y Ft(\255)246
b Fy([)308 b(])18219 43877 y Fv(B)19412 43711 y Ft(\255)246
b Fy([)308 b(])21441 43877 y Fv(B)22388 43711 y Ft(\255)11140
45371 y(\255)246 b Fy([\()p Ft(ff)p Fw(N)121 b Ft(g)15653
45537 y Fv(E)16404 45371 y Fw(;)184 b(B)56 b Ft(g)18344
45537 y Fv(E)19092 45371 y Fw(=)p Ft(f)p Fw(z)49 b(;)184
b(B)56 b Ft(g)p 22702 45065 V 337 x Fv(E)23451 45371
y Fy(\)\()p Fw(z)49 b(=)p Ft(f)p Fw(s)p Ft(g)p 27053
45065 V 337 x Fv(E)27803 45371 y Fy(\)])28540 45537 y
Fv(E)8927 47032 y Ff(BB)245 b Fy([)308 b(])11816 47198
y Fv(A)12968 47032 y Ft(\255)246 b Fy([)308 b(])14997
47198 y Fv(B)16190 47032 y Ft(\255)246 b Fy([)308 b(])18219
47198 y Fv(B)19412 47032 y Ft(\255)246 b Fy([)308 b(])21441
47198 y Fv(B)22388 47032 y Ft(\255)11140 48692 y(\255)246
b Fy([\()p Ft(f)p Fw(N)121 b Ft(g)15100 48858 y Fv(E)15850
48692 y Fw(=)p Ft(f)p Fw(s)p Ft(g)p 18028 48386 V 337
x Fv(E)18777 48692 y Fy(\)])19514 48858 y Fv(E)8927 50353
y Ff(BB)245 b Fy([)308 b(])11816 50519 y Fv(A)12968 50353
y Ft(\255)246 b Fy([)308 b(])14997 50519 y Fv(B)16190
50353 y Ft(\255)246 b Fy([)308 b(])18219 50519 y Fv(B)19412
50353 y Ft(\255)246 b Fy([)308 b(])21441 50519 y Fv(B)22634
50353 y Ft(\255)246 b Fy([)308 b(])24663 50519 y Fv(E)9631
55356 y FO(Ov)-67 b(a)67 b(j)393 b(zamara)67 b(ju)-34
b(\266)-572 b(ci)395 b(primjer)e(demonstrira)i(k)-67
b(ak)-34 b(o)393 b(se)h(izvr)-64 b(\267)-542 b(sa)-34
b(v)-67 b(a)67 b(ju)394 b(reak)-34 b(cije,)395 b(i)f(k)-67
b(ak)-34 b(o)7749 56862 y(se)545 b(de\257nira)67 b(ju)547
b(uljezo)-34 b(v)g(e)545 b(ak)-34 b(cije.)962 b(Prvi)545
b(niz)g(reak)-34 b(cija)544 b(o)34 b(dgo)-34 b(v)-67
b(ara)546 b(regularno)67 b(j)546 b(rundi)7749 58367 y(za)-34
b(\267)-572 b(cetnik)-67 b(a)502 b FG(A)i FO(s)g(o)34
b(dzivnik)-34 b(om)503 b FG(B)61 b FO(.)837 b(Uo)-34
b(\267)-572 b(cimo)503 b(da,)529 b(uk)-34 b(olik)g(o)503
b(uljez)470 b(\267)-572 b(zeli)502 b(ugrabiti)i(neku)7749
59873 y(p)34 b(oruku)493 b(s)h(mre)-34 b(\267)-572 b(ze)492
b(i)h(k)-67 b(asnije)493 b(dopustiti)i(da)f(je)f(p)34
b(o)-64 b(\267)-542 b(steni)494 b(sudionik)g(tak)-34
b(o)p 41636 59259 364 53 v(der)494 b(pro)-34 b(\267)-572
b(cita,)7749 61378 y(mora)388 b(je)g(primiti)g(i)g(nak)-34
b(on)390 b(toga)e(op)34 b(et)389 b(p)34 b(oslati.)533
b(U)389 b(mo)34 b(delu)388 b(niti)g(uljez)h(se)f(p)34
b(ona)-64 b(\267)-542 b(sa)389 b(na)7749 62884 y(isti)373
b(na)-34 b(\267)-572 b(cin.)529 b(T)-101 b(amo)374 b(je)g(to)g(o)34
b(dre)p 22131 62270 V(deno)374 b(injektivno)-64 b(\267)-542
b(s)-34 b(\266)-572 b(cu)374 b(relacije)e FI(\241)-202
b(!)p FO(,)380 b(o)-34 b(vdje)374 b(je)g(to)g(na)-34
b(\267)-572 b(cin)7749 64389 y(na)375 b(k)-34 b(o)67
b(ji)375 b(strune)h(reagira)67 b(ju.)529 b(Ak)-34 b(o)375
b(uljez)341 b(\267)-572 b(zeli)374 b(da)h FG(B)436 b
FO(pro)-34 b(\267)-572 b(cita)375 b(p)34 b(oruku)375
b(k)-34 b(o)67 b(ju)376 b(je)f(ukrao)g(s)7749 65894 y(mre)-34
b(\267)-572 b(ze,)389 b(nak)-34 b(on)388 b(reak)-34 b(cije)387
b(u)h(k)-34 b(o)67 b(jo)g(j)389 b(uljez)e(primi)g(p)34
b(oruku)388 b(o)34 b(d)387 b FG(A)324 b FO(\267)-542
b(salje)387 b(tu)h(istu)g(p)34 b(oruku,)7749 67400 y(pa)404
b(mo)-34 b(\267)-572 b(ze)404 b(reagirati)f(s)h FG(B)61
b FO(-o)-34 b(v)g(om)405 b(strunom.)7749 68905 y(Slijedi)592
b(sesija)g(izme)p 17692 68292 V(du)g(agenata)g FG(E)662
b FO(i)592 b FG(B)61 b FO(,)638 b FG(B)654 b FO(u)592
b(roli)f(o)34 b(dzivnik)-67 b(a,)637 b(a)592 b FG(E)662
b FO(kriv)-34 b(otv)g(ori)7749 70411 y(prvu)480 b(p)34
b(oruku,)436 b(\267)-542 b(sifrira)67 b(ju)-34 b(\266)-572
b(ci)480 b FI(ff)p FG(N)132 b FI(g)23769 70599 y FF(B)24578
70411 y FG(;)202 b(A)p FI(g)26632 70599 y FF(B)27921
70411 y FO(iz)479 b(prv)-34 b(e)480 b(sesije)g(agenata)h
FG(A)g FO(i)f FG(B)541 b FO(za)67 b(jedno)7749 71916
y(sa)505 b(sv)-34 b(o)67 b(jim)505 b(imenom.)840 b(Nak)-34
b(on)442 b(\267)-542 b(sto)505 b(o)-34 b(v)-67 b(a)505
b(sesija)f(za)-34 b(vr)-64 b(\267)-542 b(si,)529 b FG(E)575
b FO(p)34 b(osjeduje)506 b FI(f)p FG(N)132 b FI(g)43359
72104 y FF(B)44167 71916 y FO(,)530 b(a)505 b(jo)-64
b(\267)-542 b(s)27068 74956 y(74)p eop end end
%%Page: 75 75
TeXDict begin HPSdict begin 75 74 bop 2435 7181 a FO(jednom)405
b(sesijom)g(s)f(o)34 b(dzivnik)-34 b(om)403 b FG(B)466
b FO(dolazi)403 b(do)i(soli)f FG(N)132 b FO(.)2435 10919
y FH(6.3)1793 b(Sv)-50 b(o)100 b(jstv)-100 b(a)599 b(protok)-50
b(ola)2435 13625 y FO(Sp)34 b(eci\257k)-67 b(acija)361
b(protok)-34 b(ola)363 b(strunama)g(p)34 b(osti)-34 b(\267)-572
b(ze)361 b(isti)h(efekt)g(k)-67 b(ao)361 b(i)h(ona)g(modelom)g(trans-)
2435 15130 y(formacije)422 b(m)-34 b(ultiskup)34 b(o)-34
b(v)-67 b(a)422 b(ili)f(mo)34 b(delom)421 b(niti.)591
b(Sv)-67 b(a)422 b(tri)f(mo)34 b(dela)421 b(na)h(istom)g(su)g(niv)-34
b(ou)2435 16636 y(apstrak)g(cije,)481 b(mo)34 b(del)466
b(protok)-34 b(ola)466 b(uvijek)f(re\260ektira)g(ista)h(sv)-34
b(o)67 b(jstv)-67 b(a)467 b(protok)-34 b(ola.)723 b(Evi-)2435
18141 y(den)-34 b(tna)357 b(je)d(paralela)g(mo)34 b(dela)355
b(struna)h(s)e(mo)34 b(delom)355 b(niti:)480 b(\267)-572
b(cini)354 b(se)g(da)h(je)g(jedina)g(razlik)-67 b(a)2435
19647 y(u)532 b(prezizno)e(form)-34 b(ulirano)67 b(j)532
b(seman)-34 b(tici)532 b(prostora)f(struna,)500 b(\267)-542
b(sto)531 b(bi)g(trebalo)g(olak)-64 b(\267)-542 b(sati)2435
21152 y(zaklju)-34 b(\267)-572 b(civ)-67 b(anje)404 b(o)g(op)-34
b(\266)-572 b(cim)404 b(sv)-34 b(o)67 b(jstvima)405 b(protok)-34
b(ola.)4317 24163 y(Sljede)g(\266)-572 b(ci)318 b(k)-34
b(oncepti)319 b(olak)-64 b(\267)-542 b(sa)-34 b(v)-67
b(a)67 b(ju)319 b(rasu)p 21746 23549 364 53 v(div)-67
b(anje)319 b(o)g(protok)-34 b(olima)319 b(i)f(izvr)-64
b(\267)-542 b(senjima)318 b(pro-)2435 25668 y(tok)-34
b(ola.)2435 27984 y FL(De\257nicija)465 b(28)606 b FO(Doga)p
13659 27370 V(da)67 b(j)311 b FK(je)e(p)-62 b(otpuno)308
b(instancir)-62 b(ana)308 b(akcija.)514 b FO(T)-101 b(rag)310
b FK(je)f(niz)g(do)-62 b(ga)p 40609 27370 372 53 v(daja)2435
29489 y(koje)432 b(je)h(agent)g(izvr)-62 b(\267)-558
b(sio)431 b(u)j(rundi)f(pr)-62 b(otokola.)4317 31805
y FO(Ob)67 b(jedinjuju)-34 b(\266)-572 b(ci)408 b(sv)-34
b(e)406 b(trago)-34 b(v)g(e)406 b(agenata)h(k)-34 b(o)67
b(ji)407 b(su)f(se)g(dogo)34 b(dili)406 b(u)g(danom)h(prostoru)2435
33310 y(struna)583 b(sa)e(zadanom)i(inicijalnom)e(k)-34
b(on\257guracijom,)627 b(zapisat)548 b(\266)-572 b(cemo)580
b(sv)-34 b(e)582 b(reak)-34 b(cije)2435 34815 y(nek)g(og)509
b(izvr)-64 b(\267)-542 b(senja)507 b(protok)-34 b(ola.)851
b(Stoga,)535 b(trago)-34 b(vi)475 b(\266)-572 b(ce)507
b(nam)h(slu)-34 b(\267)-572 b(ziti)508 b(za)g(p)34 b(ohranjiv)-67
b(anje)2435 36321 y(p)34 b(o)g(datak)-67 b(a)405 b(o)f(doga)p
11484 35707 364 53 v(da)67 b(jima)405 b(u)g(nek)-34 b(o)67
b(j)405 b(egzekuciji)e(protok)-34 b(ola.)2435 37826 y(Na)414
b(primjer,)i(u)f(k)-34 b(orektno)67 b(j)414 b(rundi)h(Dolev-Y)-101
b(ao)413 b(protok)-34 b(ola,)417 b(sa)d(o)34 b(dzivnik)-34
b(om)413 b FG(B)61 b FO(,)417 b(trag)2435 39332 y(za)-34
b(\267)-572 b(cetnik)-67 b(a)404 b FG(A)g FO(bio)g(je:)2611
41536 y([\()p FG(\272)77 b(N)132 b FO(\))p FI(hff)p FG(N)g
FI(g)9067 41724 y FF(B)9877 41536 y FG(;)202 b(A)p FI(g)11931
41724 y FF(B)12740 41536 y FI(i)p FO(\()p FI(ff)p FG(N)132
b FI(g)16606 41724 y FF(A)17367 41536 y FG(;)202 b(B)61
b FI(g)19492 41724 y FF(A)20252 41536 y FO(\)\()p FI(ff)p
FG(N)132 b FI(g)24118 41724 y FF(A)24879 41536 y FG(;)202
b(B)61 b FI(g)27004 41724 y FF(A)27764 41536 y FG(=)p
FI(f)p FG(y)43 b(;)202 b(B)61 b FI(g)p 31738 41199 761
40 v 387 x FF(A)32499 41536 y FO(\)\()p FI(f)p FG(N)132
b FI(g)35759 41724 y FF(A)36520 41536 y FG(=)p FI(f)p
FG(N)g FI(g)p 39444 41199 V 387 x FF(A)40205 41536 y
FO(\)])41013 41724 y FF(A)41773 41536 y FG(;)2435 43741
y FO(dok)368 b(se)f(niz)h(doga)p 10775 43127 364 53 v(da)67
b(ja)369 b(za)f FG(B)428 b FO(u)368 b(lo)-64 b(\267)-542
b(so)67 b(j)369 b(rundi)f(protok)-34 b(ola)368 b(sasto)67
b(ji)369 b(o)34 b(d)367 b(traga)h(sesije)f(s)h FG(A)p
FO(,)2435 45247 y(i)404 b(dv)-67 b(a)404 b(traga)g(sesija)g(s)h
FG(E)70 b FO(,)403 b(u)h(k)-34 b(o)67 b(jima)405 b(je)f
FG(B)466 b FO(sv)-67 b(aki)403 b(put)i(u)f(ulozi)g(o)34
b(dzivnik)-67 b(a.)4317 48258 y(Zapis)440 b FG(E)70 b(V)270
b(E)70 b(N)132 b(T)168 b FO(\()p FG(R)9 b(;)202 b(A;)g(Q;)17289
48034 y(~)17365 48258 y(t;)186 b(~)-590 b(x)p FO(\))440
b(ozna)-34 b(\267)-572 b(ca)-34 b(v)-67 b(a)441 b(da)f(je)h
FG(A)f FO(izvr)-64 b(\267)-542 b(sio)439 b(ak)-34 b(ciju)441
b FG(Q)f FO(u)h(rundi)2435 49763 y FG(R)9 b FO(,)405
b(i)f(pritom)g(su)h(v)-67 b(arijable)386 b FG(~)-589
b(x)403 b FO(supstituirane)j(termima)28460 49539 y FG(~)28536
49763 y(t)p FO(:)6335 51968 y FG(E)70 b(V)269 b(E)70
b(N)132 b(T)168 b FO(\()p FG(R)9 b(;)202 b(A;)g(Q;)16031
51744 y(~)16107 51968 y(t)q(;)186 b(~)-590 b(x)p FO(\))337
b FI(\264)f FO([)p FG(S)70 b(QS)22786 51467 y FE(0)23097
51968 y FO(])23434 52156 y FF(A)24665 51968 y FI(\255)269
b FG(C)424 b FA(BB)336 b FO([)p FG(S)70 b(S)31352 51467
y FE(0)31663 51968 y FO(\()32058 51744 y FG(~)32134 51968
y(t=)-16 b(~)-590 b(x)p FO(\)])34679 52156 y FF(A)35910
51968 y FI(\255)269 b FG(C)38075 51467 y FE(0)2435 54172
y FO(gdje)405 b(reak)-34 b(cije)403 b([)p FG(S)70 b(QS)12363
53732 y FE(0)12674 54172 y FO(])13011 54360 y FF(A)14242
54172 y FI(\255)269 b FG(C)424 b FA(BB)336 b FO([)p FG(S)70
b(S)20929 53732 y FE(0)21240 54172 y FO(\()21635 53949
y FG(~)21711 54172 y(t=)-16 b(~)-590 b(x)p FO(\)])24256
54360 y FF(A)25487 54172 y FI(\255)269 b FG(C)27652 53732
y FE(0)28367 54172 y FO(pripada)67 b(ju)406 b(rundi)e
FG(R)9 b FO(.)2435 55678 y(T)-101 b(ak)-34 b(o)337 b(u)g(prv)-34
b(om)336 b(k)-34 b(oraku)337 b(Dolev-Y)-101 b(ao)335
b(protok)-34 b(ola)337 b(inicijator)f FG(A)p FO(,)350
b(k)-34 b(o)67 b(ji)336 b(zap)34 b(o)-34 b(\267)-572
b(cinje)336 b(sesiju)2435 57183 y(s)404 b(agen)-34 b(tom)406
b FG(B)61 b FO(,)404 b(u)g(rundi)h FG(R)9 b FO(,)404
b(kreira)f(sol:)15258 59388 y FG(E)70 b(V)269 b(E)70
b(N)132 b(T)168 b FO(\()p FG(R)9 b(;)202 b(A;)g FO(\()p
FG(\272)77 b(x)p FO(\))p FG(;)202 b(N)65 b(;)202 b(x)p
FO(\))p FG(;)2435 61592 y FO(drugi)405 b(je)f(k)-34 b(orak)404
b(slanje)g(p)34 b(oruk)-34 b(e)404 b(za)g(agen)-34 b(ta)405
b FG(B)61 b FO(:)12912 63797 y FG(E)70 b(V)269 b(E)70
b(N)132 b(T)168 b FO(\()p FG(R)9 b(;)202 b(A;)g FI(hff)p
FG(N)132 b FI(g)24582 63985 y FF(B)25392 63797 y FG(;)202
b(A)p FI(g)27446 63985 y FF(E)28241 63797 y FI(i)p FG(;)g
FI(;)p FG(;)g FI(;)p FO(\))p FG(;)2435 66002 y FO(dok)405
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FF(B)29021 68206 y FG(;)202 b(A)p FI(g)p 31075 67868
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FG(R)9 b FO(.)21755 74956 y(75)p eop end end
%%Page: 76 76
TeXDict begin HPSdict begin 76 75 bop 7749 7181 a FL(De\257nicija)465
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b(a)-34 b(\267)-572 b(ze)498 b(da)i(jedini)g(agen)-34
b(t)500 b(k)-34 b(o)67 b(ji)500 b(mo)-34 b(\267)-572
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b(telepatije\))337 b FK(Neka)f(je)g FG(R)347 b FK(runda)336
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FK(,)638 b(gdje)595 b(se)g(neke)h FG(\275)47224 29877
y FF(i)7749 31201 y FK(eventualno)406 b(p)-62 b(onavljaju,)410
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b(termu)g FG(m)i FK(agent)d FG(A)j FK(ili)e(kr)-62 b(eir)g(ao)360
b(u)h FG(\275)25155 34409 y FF(k)25724 34212 y FK(,)376
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b(an.)7749 36587 y(Dokaz.)492 b FO(Role)269 b(su)h(prede\257nirane)f
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44371 372 53 v(du)h(strunama)g(u)i FG(C)87 b FK(,)9837
47250 y FG(E)70 b(V)269 b(E)70 b(N)132 b(T)168 b FO(\()p
FG(R)9 b(;)202 b(A;)g FO(\()p FI(f)p FG(t)p FI(g)20233
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23554 46912 809 40 v 387 x FF(B)24363 47250 y FO(\))p
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b FG(H)98 b(O)34 b(N)132 b(E)70 b(S)g(T)168 b FO(\()p
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b(uzorak)-67 b(a,)531 b(\()p FI(f)p FG(t)p FI(g)24783
51319 y FF(B)25591 51131 y FG(=)p FI(f)p FG(x)p FI(g)p
28102 50794 V 387 x FF(B)28911 51131 y FO(\),)g(tada)507
b(ta)67 b(j)507 b(netk)-34 b(o)506 b(ima)g(klju)-34 b(\267)-572
b(c)p 44058 50158 981 49 v 505 w FG(B)61 b FO(.)844 b(T)-101
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b(biti)h(uljez,)h(zb)34 b(og)410 b FG(B)f FI(2)348 b
FG(H)98 b(O)34 b(N)132 b(E)70 b(S)g(T)168 b FO(\()p FG(C)87
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b(t)411 b(osim)7749 54142 y(agen)-34 b(ta)571 b FG(B)632
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b(t)351 b(p)34 b(osjeduje)351 b(ne)f(mijenja)h(se)e(u)i(tijeku)f(izvr)
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b(o)486 b(je)g(o)-34 b(v)-67 b(a)67 b(j)487 b(mo)34 b(del)485
b(predvi)p 35652 58045 364 53 v(den)h(za)g(klasu)g(protok)-34
b(ola)7749 60164 y(k)g(o)67 b(ji)543 b(ne)g(izmjenjuju)h(priv)-67
b(atne)542 b(klju)-34 b(\267)-572 b(cev)-34 b(e)542 b(me)p
29615 59551 V(du)h(sudionicima,)578 b(slanje)543 b(klju)-34
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b(ca)404 b(ak)-34 b(cija.)539 b FA(\244)7749 65417 y
FH(6.4)1792 b(Logi)-50 b(\267)-847 b(ck)-100 b(a)599
b(p)50 b(o)g(dr)-95 b(\267)-802 b(sk)-100 b(a)7749 68123
y FL(Sin)-39 b(taksa)7749 70411 y FO(Logik)-67 b(a)534
b(za)h(rasu)p 15942 69797 V(div)-67 b(anje)536 b(o)f(sv)-34
b(o)67 b(jstvima)536 b(protok)-34 b(ola)536 b(je)g(logik)-67
b(a)534 b(prv)-34 b(og)536 b(reda,)567 b(s)536 b(jed-)7749
71916 y(nim)d(do)34 b(datnim)534 b(mo)34 b(dalnim)533
b(op)34 b(eratorom.)925 b(Rje)-34 b(\267)-572 b(cnik)533
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b(ck)-67 b(a)531 b(sim)-34 b(b)34 b(ola,)27068 74956
y(76)p eop end end
%%Page: 77 77
TeXDict begin HPSdict begin 77 76 bop 2435 7181 a FI(^)p
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b(ci)469 b FI(\241)-202 b(!)p FG(;)202 b FI(_)p FG(;)g
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b FG(\301)416 b FO(je)g(induktivno)g(izgra)p 18442 8073
364 53 v(dena)g(k)-67 b(ao)415 b(k)-34 b(onjunk)g(cija,)420
b(negacija)415 b(ili)g(univ)-34 b(erzalna)2435 10192
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b(cih)404 b(predik)-67 b(ata:)4253 12796 y FI(\262)607
b FN(Kno)-34 b(ws)p FO(\()p FG(a;)202 b(t)p FO(\))4253
15400 y FI(\262)607 b FN(Sent)p FO(\()p FG(a;)202 b(t)p
FO(\))4253 18004 y FI(\262)607 b FN(Decrypts)o FO(\()p
FG(a;)202 b(t)p FO(\))4253 20608 y FI(\262)607 b FN(Honest)o
FO(\()p FG(a)p FO(\))4253 23212 y FI(\262)g FN(Source)p
FO(\()p FG(n;)202 b(a;)g(t;)g(k)38 b FO(\))2435 25816
y(gdje)360 b(je)f FG(a)g FO(ime,)367 b FG(t)359 b FO(term,)367
b FG(n)359 b FO(sol,)368 b FG(k)397 b FO(ja)-34 b(vni)360
b(klju)-34 b(\267)-572 b(c,)367 b(k)-67 b(ao)359 b(u)g(jeziku)g(ra)-34
b(\267)-572 b(cuna)359 b(pro)34 b(cesa)359 b(iz)f(6.1.)4317
28852 y(Ciljana)476 b(seman)-34 b(tik)-67 b(a)475 b(form)-34
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FO(\))475 b(je:)680 b(agen)-34 b(t)476 b FG(a)e FO(zna)h(p)34
b(o)g(datak)475 b FG(t)p FO(.)751 b(Mo-)2435 30358 y(gao)613
b(ga)h(je)f(kreirati,)663 b(primiti)613 b(u)g(tijeku)h(izvr)-64
b(\267)-542 b(senja)612 b(runde)i(protok)-34 b(ola,)665
b(ili)612 b(s)h(njim)2435 31863 y(biti)476 b(inicijaliziran,)493
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b(ad)476 b(je)g FG(t)g FO(ime,)493 b(o)34 b(dnosno)477
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b(o)476 b(vrijedi)2435 33369 y FN(Kno)-34 b(ws)q FO(\()p
FG(a;)202 b(t)p FO(\))485 b(onda)i(term)e FG(t)g FO(nije)h(priv)-67
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b(cije)399 b({)2435 36379 y(ak)-34 b(o)353 b(je)g(primio)f
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b(ciju.)2435 37885 y FN(Sent)p FO(\()p FG(a;)202 b(t)p
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FG(a)f FO(p)34 b(oslao)405 b(p)34 b(oruku)404 b FG(t)p
FO(;)f(za)h(to)h(je)f(pretho)34 b(dno)405 b(morao)f(znati)h
FG(t)p FO(.)2435 39390 y(Ak)-34 b(o)404 b(je)g FN(Decrypts)o
FO(\()p FG(a;)202 b(t)p FO(\))404 b(istinito)f(za)h FG(a)p
FO(,)f(tada)h(je)g FG(a)f FO(primio)g(enkrip)34 b(ciju)403
b FG(t)g FO(k)-34 b(o)67 b(ju)405 b(je)f(mo-)2435 40896
y(gao)409 b(de)-64 b(\267)-542 b(sifrirati.)550 b(T)-101
b(o)408 b(p)34 b(o)-34 b(vla)g(\267)-572 b(ci)408 b(da)g
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b(cije)407 b(zna)h(i)g(p)34 b(oruku)408 b(k)-34 b(o)67
b(ja)2435 42401 y(je)404 b(bila)340 b(\267)-542 b(sifrirana.)2435
43907 y(Za)421 b(agen)-34 b(ta)421 b FG(a)g FO(sv)-34
b(o)67 b(jstv)-34 b(o)422 b FN(Honest)o FO(\()p FG(a)p
FO(\))f(zna)-34 b(\267)-572 b(ci)420 b(da)h(njego)-34
b(v)421 b(priv)-67 b(atni)421 b(klju)-34 b(\267)-572
b(c)420 b(uljez)h(ne)g(p)34 b(os-)2435 45412 y(jeduje,)405
b(o)34 b(dnosno,)405 b(da)f FG(a)g FO(izv)-34 b(o)34
b(di)404 b(samo)g(ak)-34 b(cije)404 b(o)34 b(dre)p 26788
44799 V(dene)404 b(protok)-34 b(olom.)2435 46918 y(F)-101
b(orm)-34 b(ula)485 b FN(Source)p FO(\()p FG(n;)202 b(a;)g(t;)g(k)38
b FO(\))450 b(\266)-572 b(ce)483 b(vrijediti)g(ak)-34
b(o)484 b(je)h(agen)-34 b(t)485 b FG(a)e FO(stv)-34 b(orio)484
b(p)34 b(oruku)485 b FI(f)p FG(t)p FI(g)40560 47115 y
FF(k)41612 46918 y FO(u)2435 48423 y(k)-34 b(o)67 b(jo)g(j)439
b(je)f FG(n)f FO(p)34 b(o)g(dterm)438 b(o)34 b(d)437
b FG(t)p FO(,)446 b(i)437 b(jedini)h(na)-34 b(\267)-572
b(cin)437 b(da)h(neki)f(drugi)h(agen)-34 b(t)439 b(do)p
35793 47810 V(de)f(do)g FG(n)f FO(je)g(iz)2435 49929
y(p)34 b(oruk)-34 b(e)366 b FI(f)p FG(t)p FI(g)8057 50126
y FF(k)8626 49929 y FO(,)373 b(njenim)367 b(dekriptiranjem)f(ili)e
(indirektno,)374 b(tak)-34 b(o)302 b(\267)-542 b(sto)367
b(ju)f(je)g(netk)-34 b(o)367 b(drugi)2435 51434 y(dekriptirao)510
b(i)g(p)34 b(oslao)510 b FG(n)f FO(u)h(nek)-34 b(o)67
b(j)511 b(drugo)67 b(j)512 b(p)34 b(oruci.)856 b(T)-101
b(ak)-34 b(o)p 30631 50821 V(der,)536 b FG(a)510 b FO(je)g(generirao)f
(sol)2435 52940 y FG(n)481 b FO(op)34 b(eratorom)481
b(\()p FG(\272)77 b(x)p FO(\))481 b(i)g(p)34 b(oslao)481
b(je)g(jednom,)500 b(u)482 b FI(f)p FG(t)p FI(g)26560
53137 y FF(k)27128 52940 y FO(.)769 b(Nije)481 b(ju)h(p)34
b(oslao)481 b(na)g(nek)-34 b(olik)g(o)2435 54445 y(adresa)404
b(u)h(raznim)f(p)34 b(oruk)-67 b(ama,)403 b(nego)i(jednom)g(sugo)-34
b(v)g(orniku)405 b(u)f(jedno)67 b(j)406 b(p)34 b(oruci.)2435
55951 y(Relacija)404 b(p)34 b(o)g(dterm,)404 b FI(v)p
FO(,)f(iden)-34 b(ti)g(\267)-572 b(cna)405 b(je)f(ono)67
b(j)406 b(iz)d(mo)34 b(dela)404 b(niti)g(\(strana)h(44\).)4317
58987 y(Ovi)326 b(predik)-67 b(ati,)341 b(i)326 b(predik)-67
b(atne)326 b(form)-34 b(ule,)342 b(izri)-34 b(\267)-572
b(cu)326 b(sv)-34 b(o)67 b(jstv)-67 b(a)327 b(o)g(agen)-34
b(tima)327 b(i)f(njiho)-34 b(vim)2435 60492 y(ak)g(cijama,)397
b(u)e(jednom)h(tren)-34 b(utku)396 b(izvr)-64 b(\267)-542
b(senja)394 b(protok)-34 b(ola.)536 b(Za)395 b(form)-34
b(uliranje)395 b(tvrdnji)h(o)2435 61998 y(sv)-34 b(o)67
b(jstvima)454 b(\267)-572 b(cija)485 b(istinitost)i(o)-34
b(visi)485 b(o)h(nizu)g(pretho)34 b(dno)487 b(izvr)-64
b(\267)-542 b(senih)485 b(ak)-34 b(cija)486 b(k)-34 b(oristimo)2435
63503 y(form)g(ule)405 b(oblik)-67 b(a:)20637 65086 y([)p
FG(Q)p FO(])22269 65268 y FF(a)23026 65086 y FG(\301;)2435
67400 y FO(gdje)407 b(je)e FG(\301)h FO(predik)-67 b(atna)406
b(form)-34 b(ula.)545 b(Zna)-34 b(\267)-572 b(cenje)406
b(je)f(mo)34 b(dalno:)543 b(ak)-34 b(o)406 b(je)g(runda)g(protok)-34
b(ola)2435 68905 y(u)535 b(stanju)g(gdje)f(je)g FG(a)g
FO(v)-34 b(e)g(\266)-572 b(c)533 b(izvr)-64 b(\267)-542
b(sio)533 b(niz)g(ak)-34 b(cija)534 b FG(Q)p FO(,)566
b(tada)535 b(je)f(predik)-67 b(atna)534 b(form)-34 b(ula)535
b FG(\301)2435 70411 y FO(istinita.)527 b(Ov)-67 b(a)366
b(forma)h(mo)34 b(dalne)367 b(form)-34 b(ule)367 b(je)f(fundamen)-34
b(talna)370 b(u)d(dok)-67 b(aziv)g(anju)367 b(sv)-34
b(o)67 b(js-)2435 71916 y(ta)-34 b(v)-67 b(a)405 b(protok)-34
b(ola.)21755 74956 y(77)p eop end end
%%Page: 78 78
TeXDict begin HPSdict begin 78 77 bop 7749 7181 a FL(Seman)-39
b(tik)-77 b(a)7749 9470 y FO(Induktivno)457 b(de\257niramo)f(k)-67
b(ada)456 b(je)g(form)-34 b(ula)457 b FG(\301)f FO(k)-34
b(o)67 b(ja)457 b(nema)f(slob)34 b(o)g(dnih)456 b(v)-67
b(arijabli)455 b(is-)7749 10975 y(tinita)404 b(u)h(rundi)g
FG(R)413 b FO(protok)-34 b(ola)405 b FG(P)168 b FO(,)340
b(\267)-542 b(sto)405 b(pi)-64 b(\267)-542 b(semo)404
b FG(P)34 b(;)202 b(R)346 b FA(\262)336 b FG(\301)p FO(.)7749
12480 y(Ak)-34 b(o)301 b FG(\301)h FO(sadr)-34 b(\267)-572
b(zi)301 b(slob)34 b(o)g(dne)302 b(v)-67 b(arijable,)321
b(onda)302 b FG(P)34 b(;)202 b(R)346 b FA(\262)337 b
FG(\301)301 b FO(ak)-34 b(o)302 b FG(P)34 b(;)202 b(R)346
b FA(\262)336 b FG(\276)43 b(\301)302 b FO(za)f(sv)-34
b(e)302 b(p)34 b(otpune)7749 13986 y(supstitucije)405
b FG(\276)43 b FO(.)9567 16270 y FI(\262)606 b FG(P)34
b(;)202 b(R)346 b FA(\262)336 b FN(Kno)-34 b(ws)q FO(\()p
FG(a;)202 b(t)p FO(\))404 b(je)g(de\257nirano)h(induktivno:)10779
17775 y FG(P)34 b(;)202 b(R)680 b FA(\262)670 b FN(Kno)-34
b(ws)q FO(\()p FG(a;)202 b(t)p FO(\))604 b(ak)-34 b(o)604
b FG(t)671 b FI(2)f FG(f)130 b(v)43 b FO(\()p FG(R)9
b FI(j)29739 17957 y FF(a)30296 17775 y FO(\))605 b(ili)e
FG(E)70 b(V)269 b(E)70 b(N)132 b(T)168 b FO(\()p FG(R)9
b(;)202 b(a;)g FO(\()p FG(\272)77 b(x)p FO(\))p FG(;)202
b(t;)g(x)p FO(\))605 b(ili)10779 19281 y FG(E)70 b(V)269
b(E)70 b(N)132 b(T)168 b FO(\()p FG(R)9 b(;)202 b(a;)g
FO(\()p FG(x)p FO(\))p FG(;)g(t;)g(x)p FO(\))10779 22746
y FG(P)34 b(;)202 b(R)346 b FA(\262)336 b FN(Kno)-34
b(ws)q FO(\()p FG(a;)202 b(t)p FO(\))404 b(ak)-34 b(o)13446
25161 y(\()p FG(P)34 b(;)202 b(R)346 b FA(\262)337 b
FN(Kno)-34 b(ws)p FO(\()p FG(a;)202 b(t)23034 24721 y
FE(0)23344 25161 y FO(\))404 b(i)g FG(t)25398 24721 y
FE(0)26045 25161 y FO(=)337 b FG(p)p FO(\()p FG(t)p FO(\))404
b(i)13446 26666 y FG(E)70 b(V)269 b(E)70 b(N)132 b(T)168
b FO(\()p FG(R)9 b(;)202 b(a;)g FO(\()p FG(p)p FO(\()p
FG(t;)23906 26443 y(~)23982 26666 y(t)p FO(\))p FG(=p)p
FO(\()p FG(x;)186 b(~)-590 b(x)p FO(\)\))p FG(;)202 b
FO(\()p FG(t;)31356 26443 y(~)31432 26666 y(t)p FO(\))p
FG(;)g FO(\()p FG(x;)186 b(~)-590 b(x)p FO(\)\)\))14254
28172 y(ili)13446 30033 y(\()p FG(P)34 b(;)202 b(R)346
b FA(\262)337 b FN(Kno)-34 b(ws)p FO(\()p FG(a;)202 b(t)23034
29593 y FE(0)23344 30033 y FO(\))404 b(i)g FG(t)25398
29593 y FE(0)26045 30033 y FO(=)337 b FI(f)p FG(p)p FO(\()p
FG(t;)29913 29809 y(~)29989 30033 y(t)o FO(\))p FI(g)31503
30221 y FF(K)32819 30033 y FO(i)13446 31539 y FG(E)70
b(V)269 b(E)70 b(N)132 b(T)168 b FO(\()p FG(R)9 b(;)202
b(a;)g FO(\()p FI(f)p FG(p)p FO(\()p FG(t;)24512 31315
y(~)24588 31539 y(t)p FO(\))p FI(g)26103 31736 y FF(k)26673
31539 y FO(\))p FG(=)p FI(f)p FG(p)p FO(\()p FG(x;)186
b(~)-590 b(x)p FO(\))p FI(g)p 32439 31201 569 40 v 396
x FF(k)33008 31539 y FO(\))p FG(;)202 b FO(\()p FG(t;)35390
31315 y(~)35466 31539 y(t)o FO(\))p FG(;)g FO(\()p FG(x;)186
b(~)-590 b(x)p FO(\)\)\))14254 33044 y(ili)13446 34905
y(\()p FG(P)34 b(;)202 b(R)346 b FA(\262)337 b FN(Kno)-34
b(ws)p FO(\()p FG(a;)202 b(t)23034 35087 y FB(1)23559
34905 y FO(\))377 b(i)g FG(P)34 b(;)202 b(R)346 b FA(\262)336
b FN(Kno)-34 b(ws)q FO(\()p FG(a;)202 b(t)34238 35087
y FB(2)34763 34905 y FO(\))377 b(i)g FG(t)336 b FO(=)h
FG(t)38817 35087 y FB(1)39342 34905 y FG(;)202 b(t)40319
35087 y FB(2)41221 34905 y FO(ili)376 b FG(t)337 b FO(=)f
FG(t)45100 35087 y FB(2)45626 34905 y FG(;)202 b(t)46603
35087 y FB(1)47128 34905 y FO(\))14254 36411 y(ili)13446
38272 y(\()p FG(P)34 b(;)202 b(R)346 b FA(\262)337 b
FN(Kno)-34 b(ws)p FO(\()p FG(a;)202 b(t)23034 37832 y
FE(0)23344 38272 y FO(\))404 b(i)g FG(P)34 b(;)202 b(R)346
b FA(\262)337 b FN(Kno)-34 b(ws)p FO(\()p FG(a;)202 b(k)38
b FO(\))404 b(i)g FG(t)336 b FO(=)h FI(f)p FG(t)39022
37832 y FE(0)39332 38272 y FI(g)39938 38469 y FF(k)40507
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b(R)346 b FA(\262)336 b FN(Sent)q FO(\()p FG(a;)202 b(t)p
FO(\))404 b(ak)-34 b(o)404 b FG(E)70 b(V)269 b(E)70 b(N)132
b(T)168 b FO(\()p FG(R)9 b(;)202 b(a;)g FI(h)p FG(t)p
FI(i)p FG(;)g FI(;)p FG(;)g FI(;)p FO(\))9567 43101 y
FI(\262)606 b FG(P)34 b(;)202 b(R)346 b FA(\262)336 b
FN(Decrypts)p FO(\()p FG(a;)202 b(t)p FO(\))404 b(ak)-34
b(o)404 b FG(t)337 b FO(=)f FI(f)p FG(t)27212 42661 y
FE(0)27522 43101 y FI(g)28128 43298 y FF(k)29101 43101
y FO(i)404 b FG(E)70 b(V)269 b(E)70 b(N)132 b(T)168 b
FO(\()p FG(R)9 b(;)202 b(a;)g FO(\()p FI(f)p FG(t)39364
42661 y FE(0)39676 43101 y FI(g)40282 43298 y FF(k)40850
43101 y FG(=)p FI(f)p FG(x)p FI(g)p 43361 42763 V 397
x FF(k)43930 43101 y FO(\))p FG(;)g(t)45378 42661 y FE(0)45689
43101 y FG(;)g(x)p FO(\))9567 45516 y FI(\262)606 b FG(P)34
b(;)202 b(R)570 b FA(\262)561 b FN(Honest)o FO(\()p FG(a)p
FO(\))539 b(if)f FG(a)561 b FI(2)g FG(H)98 b(O)34 b(N)132
b(E)70 b(S)g(T)168 b FO(\()p FG(C)87 b FO(\),)572 b(gdje)539
b(je)g FG(C)625 b FO(prostor)539 b(struna)h(u)10779 47021
y(k)-34 b(o)67 b(jem)405 b(je)f(runda)h FG(R)414 b FO(izv)-34
b(o)p 22882 46407 364 53 v(dena.)9567 49436 y FI(\262)606
b FG(P)34 b(;)202 b(R)346 b FA(\262)336 b FN(Source)q
FO(\()p FG(n;)202 b(a;)g(t;)g(k)38 b FO(\))403 b(ak)-34
b(o)404 b FG(E)70 b(V)269 b(E)70 b(N)132 b(T)168 b FO(\()p
FG(R)9 b(;)202 b(a;)g FO(\()p FG(\272)77 b(x)p FO(\))p
FG(;)202 b(n;)g(x)p FO(\))404 b(i)10779 50941 y FG(P)34
b(;)202 b(R)346 b FA(\262)336 b FI(8)202 b FG(b)g FO(\(\()p
FG(b)339 b FI(6)p FO(=)d FG(a)p FO(\))270 b FI(^)471
b FN(Kno)-34 b(ws)p FO(\()p FG(b;)202 b(n)p FO(\))337
b FI(\241)-202 b(!)337 b FN(Decrypts)p FO(\()p FG(b;)202
b FI(f)p FG(t)p FI(g)38135 51138 y FF(k)38704 50941 y
FO(\))p FI(_)11452 52447 y(_)270 b FO(\()p FI(9)202 b
FG(c)g FN(Decrypts)p FO(\()p FG(c;)g FI(f)p FG(t)p FI(g)22243
52644 y FF(k)22811 52447 y FO(\))270 b FI(^)f FN(Sent)p
FO(\()p FG(c;)202 b(t)28878 52007 y FE(0)29188 52447
y FO(\)\)\))10779 53952 y(gdje)405 b(je)f FG(n)336 b
FI(v)g FG(t)17466 53512 y FE(0)9567 56367 y FI(\262)606
b FG(P)34 b(;)202 b(R)542 b FA(\262)533 b FO([)p FG(Q)p
FO(])16498 56549 y FF(a)17053 56367 y FG(\301)522 b FO(ak)-34
b(o)522 b(se)g FG(Q)g FO(ne)g(p)34 b(oklapa)522 b(s)g
FG(R)9 b FI(j)32353 56549 y FF(a)32908 56367 y FO(,)551
b(ili)521 b(se)h FG(Q)g FO(p)34 b(oklapa)522 b(s)g FG(R)9
b FI(j)45310 56549 y FF(a)46387 56367 y FO(uz)10779 57872
y(supstituciju)406 b(p)34 b(oklapanja)405 b FG(\276)447
b FO(i)404 b FG(P)34 b(;)202 b(R)346 b FA(\262)336 b
FG(\276)43 b(\301)p FO(.)9567 60287 y FI(\262)606 b FG(P)34
b(;)202 b(R)346 b FA(\262)336 b FG(\301)15195 60469 y
FB(1)15991 60287 y FI(^)269 b FG(\301)17790 60469 y FB(2)18720
60287 y FO(ak)-34 b(o)405 b FG(P)34 b(;)202 b(R)346 b
FA(\262)336 b FG(\301)25359 60469 y FB(1)26289 60287
y FO(i)404 b FG(P)34 b(;)202 b(R)346 b FA(\262)336 b
FG(\301)31446 60469 y FB(2)9567 62701 y FI(\262)606 b
FG(P)34 b(;)202 b(R)346 b FA(\262)336 b FI(:)p FG(\301)405
b FO(ak)-34 b(o)404 b FG(P)34 b(;)202 b(R)346 b Fp(2)336
b FG(\301)9567 65116 y FI(\262)606 b FG(P)34 b(;)202
b(R)456 b FA(\262)447 b FI(8)p FG(x)202 b(\301)470 b
FO(ak)-34 b(o)471 b(za)f(sv)-67 b(aku)469 b(p)34 b(oruku)471
b FG(m)f FO(k)-34 b(o)67 b(ja)471 b(se)f(sasto)67 b(ji)472
b(samo)e(o)34 b(d)470 b(imena)h(i)10779 66621 y(klju)-34
b(\267)-572 b(cev)-67 b(a)412 b FG(P)34 b(;)202 b(R)360
b FA(\262)351 b FO([)p FG(m=x)p FO(])p FG(\301)p FO(.)564
b(Jasno,)416 b(o)-34 b(visno)413 b(o)f(tome)h(k)-67 b(ak)-34
b(o)413 b(je)g FG(x)f FO(uklju)-34 b(\267)-572 b(cen)413
b(u)g FG(\301)p FO(,)10779 68127 y(pro)-34 b(vjera)g(v)-67
b(amo)404 b(samo)h(nek)-34 b(e)404 b(terme.)9631 70411
y(Pi)-64 b(\267)-542 b(semo)269 b FG(P)505 b FA(\262)336
b FG(\301)270 b FO(ak)-34 b(o)270 b(je)g FG(P)34 b(;)202
b(R)346 b FA(\262)336 b FG(\301)270 b FO(za)g(sv)-34
b(e)269 b(runde)h FG(R)280 b FO(protok)-34 b(ola)270
b FG(P)438 b FO(uz)270 b(dane)g(p)34 b(o)-34 b(\267)-572
b(cetne)7749 71916 y(uvjete,)339 b(k)-34 b(o)67 b(ji)323
b(uklju)-34 b(\267)-572 b(cuju)324 b(imena)e(agenata,)339
b(strune)324 b(roli)e(protok)-34 b(ola)323 b(i)f(uljezo)-34
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end
%%Page: 79 79
TeXDict begin HPSdict begin 79 78 bop 2435 7181 a FL(Aksiomi)464
b(i)h(pra)-39 b(vila)465 b(dok)-77 b(aznog)464 b(sistema)2435
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b(vljen)g(u)538 b(logiku)d(zadan)i(je)f(aksiomima)f(\(tablice)h(6.1)g
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b(\(tablica)h(6.3)g(i)f(pra)-34 b(vilo)403 b(6.5\).)539
b(Ak)-34 b(o)403 b(je)h(nek)-67 b(a)403 b(form)-34 b(ula)404
b FG(\301)g FO(izv)-34 b(o)34 b(dljiv)-67 b(a)2435 12515
y(za)366 b(protok)-34 b(ol)367 b FG(P)535 b FO(u)367
b(dok)-67 b(aznom)367 b(sistem)-34 b(u,)374 b(pi)-64
b(\267)-542 b(semo)367 b FG(P)505 b FI(`)336 b FG(\301)p
FO(.)526 b(Izv)-34 b(o)34 b(dljiv)-34 b(ost)367 b(se)f(ugla)-34
b(vnom)2435 14020 y(promatra)424 b(za)e(k)-34 b(onkretni)423
b(protok)-34 b(ol)423 b FG(P)168 b FO(.)595 b(Sv)-34
b(o)67 b(jstv)-67 b(a)424 b(protok)-34 b(ola)423 b(o)g(k)-34
b(o)67 b(jima)423 b(go)-34 b(v)g(ore)423 b(ak-)2435 15526
y(siomi)404 b(i)g(pra)-34 b(vila)404 b(su:)4253 18099
y FI(\262)607 b FK(svojstva)482 b(zaje)-62 b(dni)-31
b(\267)-589 b(cka)483 b(svim)h(pr)-62 b(otokolima)p FO(.)705
b(T)-101 b(akv)-67 b(a)460 b(sv)-34 b(o)67 b(jstv)-67
b(a)462 b(opisuju)g(svi)e(ak-)5466 19604 y(siomi)472
b(te)g(pra)-34 b(vila)472 b(iz)g(tablice)f(6.3.)743 b(Radi)473
b(se)f(o)g(tvrdnjama)i(v)-34 b(ezanim)472 b(za)g(pre-)5466
21110 y(dik)-67 b(ate,)561 b(v)-34 b(e)g(\266)-572 b(cina)530
b(ih)h(direktno)f(re\260ektira)g(seman)-34 b(tiku)531
b(predik)-67 b(ata)530 b(i)g(o)-34 b(\267)-572 b(cigledne)5466
22615 y(o)34 b(dnose)404 b(me)p 11289 22002 364 53 v(du)h(njima.)4253
25188 y FI(\262)607 b FK(invarijante)459 b(o)-62 b(dr)g(e)p
14271 24574 372 53 v(deno)g(g)459 b(pr)-62 b(otokola)p
FO(.)626 b(Pra)-34 b(vilo)433 b(k)-34 b(o)67 b(je)435
b(se)f(o)34 b(dnosi)434 b(na)h(k)-34 b(onkretni,)5466
26693 y(p)34 b(o)67 b(jedini)380 b(protok)-34 b(ol)380
b(je)g(pra)-34 b(vilo)379 b(p)34 b(o)-64 b(\267)-542
b(stenja)381 b(\(6.5\).)531 b(T)-101 b(emelj)380 b(je)f(dok)-67
b(aziv)g(anja)380 b(sv)-34 b(o-)5466 28199 y(jsta)g(v)-67
b(a)404 b(p)34 b(o)67 b(jedinih)406 b(protok)-34 b(ola.)4317
30772 y(Dak)-67 b(ak)-34 b(o,)403 b(dok)-67 b(azni)404
b(sistem)g(je)h(smislen)e(jedino)i(ak)-34 b(o)404 b(vrijedi:)2435
33362 y FL(T)-116 b(eorem)464 b(6)606 b FK(\(Kor)-62
b(ektnost.\))554 b(A)-31 b(ko)433 b FG(P)505 b FI(`)337
b FG(\301)434 b FK(onda)e FG(P)506 b FI(j)-202 b FO(=)336
b FG(\301)p FK(.)4317 35935 y FO(P)-34 b(ozadina)554
b(sv)-67 b(ak)-34 b(og)553 b(aksioma)h(trebala)f(bi)h(biti)g(jasna:)838
b(aksiom)553 b FL(AN)37046 36117 y Fj(1)38197 35935 y
FO(k)-67 b(a)-34 b(\267)-572 b(ze)552 b(da)2435 37441
y(agen)-34 b(t)403 b(zna)f(vrijednost)g(k)-34 b(o)67
b(ju)404 b(je)d(kreirao.)537 b(Aksiom)401 b FL(AN)28697
37623 y Fj(2)29697 37441 y FO(k)-67 b(a)-34 b(\267)-572
b(ze)400 b(da)j(ak)-34 b(o)402 b(je)g FG(a)f FO(kreirao)2435
38946 y(vrijednost)486 b FG(n)p FO(,)504 b(i)484 b(netk)-34
b(o)485 b(to)h(zna,)504 b(onda)486 b(ta)67 b(j)486 b(netk)-34
b(o)485 b(mora)g(biti)g FG(a)p FO(.)780 b(Ovdje)484 b(v)-67
b(alja)485 b(biti)2435 40452 y(oprezan)304 b(i)f(imati)g(na)h(um)-34
b(u)305 b(in)-34 b(terpretaciju)304 b(o)34 b(d)303 b([\()p
FG(\272)77 b(n)p FO(\)])26848 40634 y FF(a)27403 40452
y FO(,)323 b(a)304 b(to)g(je:)488 b(\()p FG(\272)77 b(x)p
FO(\))304 b(je)f(bila)g(p)34 b(osljed-)2435 41957 y(nja)405
b(ak)-34 b(cija)404 b(o)34 b(d)404 b FG(a)p FO(,)g(gdje)g(je)h
FG(x)e FO(supstituiran)j(sa)e FG(n)p FO(.)6295 46280
y FL(AN)8440 46462 y Fj(1)13130 46280 y FO([\()p FG(\272)77
b(n)p FO(\)])16150 46462 y FF(a)16705 46280 y FN(Kno)-34
b(ws)p FO(\()p FG(a;)202 b(n)p FO(\))6295 48117 y FL(AN)8440
48299 y Fj(2)13130 48117 y FO([\()p FG(\272)77 b(n)p
FO(\)])16150 48299 y FF(a)16705 48117 y FN(Kno)-34 b(ws)p
FO(\()p FG(b;)202 b(n)p FO(\))337 b FI(\241)-202 b(!)337
b FG(b)g FO(=)f FG(a)6295 49955 y FL(AS)8123 50137 y
Fj(1)13130 49955 y FO([)p FI(h)p FG(m)p FI(i)p FO(])15810
50137 y FF(a)16366 49955 y FN(Sent)p FO(\()p FG(a;)202
b(m)p FO(\))6295 51792 y FL(AR)8394 51974 y Fj(1)13130
51792 y FO([\()p FG(m)p FO(\)])15810 51974 y FF(a)16366
51792 y FN(Kno)-34 b(ws)p FO(\()p FG(a;)202 b(m)p FO(\))6295
53630 y FL(AR)8394 53812 y Fj(2)13130 53630 y FO([\()p
FG(m)p FO(\)])15810 53812 y FF(a)16366 53630 y FI(9)g
FG(b)p FN(Sent)q FO(\()p FG(b;)g(m)p FO(\))6295 55468
y FL(AD)8418 55650 y Fj(1)13130 55468 y FO([\()p FI(f)p
FG(m)p FI(g)16214 55656 y FF(K)17126 55468 y FG(=)p FO(\)])18540
55650 y FF(a)19095 55468 y FN(Decrypts)p FO(\()p FG(a;)g
FI(f)p FG(m)p FI(g)27477 55665 y FF(k)28046 55468 y FO(\))6295
57305 y FL(AM)8672 57487 y Fj(1)13130 57305 y FO(\()p
FG(x)14294 57487 y FB(1)14820 57305 y FG(;)g(:)g(:)g(:)f(;)h(x)18207
57487 y FF(n)18833 57305 y FO(\)[)337 b(])20315 57487
y FF(a)20869 57305 y FN(Kno)-34 b(ws)q FO(\()p FG(a;)202
b(x)26547 57487 y FB(1)27072 57305 y FO(\))270 b FI(^)f
FG(:)202 b(:)g(:)269 b FI(^)g FN(Kno)-34 b(ws)q FO(\()p
FG(a;)202 b(x)37329 57487 y FF(n)37954 57305 y FO(\))6295
59143 y FL(AN)8440 59325 y Fj(3)13130 59143 y FO([\()p
FG(\272)77 b(n)p FO(\)])16150 59325 y FF(a)16705 59143
y FI(8)202 b FG(t)p FI(8)g FG(k)38 b FN(Source)q FO(\()p
FG(n;)202 b(a;)g(t;)g(k)38 b FO(\))6295 61819 y FL(S)7069
62001 y Fj(1)15753 60946 y FO([)p FG(Q)p FO(])17385 61128
y FF(a)17940 60946 y FN(Source)p FO(\()p FG(n;)202 b(a;)g(t;)g(k)38
b FO(\))p 13263 61540 15598 49 v 14172 62692 a([)p FG(Q)p
FI(hf)p FG(t)p FI(g)17588 62889 y FF(k)18157 62692 y
FI(i)p FO(])18965 62874 y FF(a)19520 62692 y FN(Source)q
FO(\()p FG(n;)202 b(a;)g(t;)g(k)38 b FO(\))28994 61819
y FG(;)606 b FO(gdje)404 b(je)g FG(n)336 b FI(v)h FG(t)14643
66272 y FO(T)-101 b(ablica)405 b(6.1:)538 b(Osno)-34
b(vni)404 b(aksiomi)4317 68905 y(Predik)-67 b(at)476
b FN(Sent)g FO(direktno)g(o)34 b(dgo)-34 b(v)-67 b(ara)476
b(ak)-34 b(ciji)476 b(slanja,)430 b(\267)-542 b(sto)477
b(je)f(o)-34 b(\267)-572 b(cito)476 b(iz)g FL(AS)38965
69087 y Fj(1)39563 68905 y FO(,)494 b(isto)2435 70411
y(k)-67 b(ao)305 b(\267)-542 b(sto)370 b(to)g FL(AD)10084
70593 y Fj(1)11051 70411 y FO(p)34 b(ok)-67 b(azuje)369
b(za)g FN(Decrypt)p FO(.)527 b(Agen)-34 b(t)370 b(k)-34
b(o)67 b(ji)370 b(je)f(primio)g(p)34 b(oruku)370 b FG(m)g
FO(zna)f(tu)2435 71916 y(p)34 b(oruku)405 b(\()p FL(AR)9184
72098 y Fj(1)9782 71916 y FO(\);)f(i)g(vi)-64 b(\267)-542
b(se,)403 b(netk)-34 b(o)405 b(ju)g(je)f(morao)g(p)34
b(oslati)404 b(\()p FL(AR)30753 72098 y Fj(2)31351 71916
y FO(\).)21755 74956 y(79)p eop end end
%%Page: 80 80
TeXDict begin HPSdict begin 80 79 bop 7749 7181 a FO(Aksiom)455
b FL(AM)14561 7363 y Fj(1)15615 7181 y FO(isk)-67 b(azuje)456
b(da)g(su)h(imena)f(i)f(klju)-34 b(\267)-572 b(cevi)455
b(k)-34 b(o)67 b(jima)457 b(je)f(agen)-34 b(t)457 b(u)f(o)34
b(dre)p 44931 6568 364 53 v(deno)67 b(j)7749 8687 y(roli)403
b(instanciran)i(p)34 b(oznati)404 b(tom)h(agen)-34 b(tu.)7749
10192 y(Pra)g(vilo)464 b(izv)-34 b(o)p 14354 9579 V(denja)466
b FL(S)18194 10374 y Fj(1)19257 10192 y FO(je)f(dano)h(u)f(o)-34
b(v)g(o)67 b(j)467 b(tablici)d(k)-67 b(ak)-34 b(o)465
b(bi)g FL(AN)37721 10374 y Fj(3)38784 10192 y FO(bio)g(promatran)h(u)
7749 11698 y(k)-34 b(on)g(tekstu)448 b(tog)e(pra)-34
b(vila.)665 b(Pra)-34 b(vilo)446 b(k)-67 b(a)-34 b(\267)-572
b(ze)445 b(da)i(je)f(p)34 b(oslana)447 b(p)34 b(oruk)-67
b(a)446 b FI(f)p FG(t)p FI(g)40308 11895 y FF(k)41323
11698 y FO(izv)-34 b(or)445 b(soli)h FG(n)p FO(.)7749
13203 y(Aksiom)405 b FL(AN)14279 13385 y Fj(3)15281 13203
y FO(je)h(bazni)f(slu)-34 b(\267)-572 b(ca)67 b(j)406
b(tog)g(induktivnog)g(pra)-34 b(vila:)540 b(ak)-34 b(o)406
b(je)f(p)34 b(osljednja)406 b(ak-)7749 14709 y(cija)373
b(agen)-34 b(ta)375 b FG(a)e FO(bila)h(stv)-67 b(aranje)373
b(soli)h FG(n)p FO(,)k(tada)d(je)f(sv)-67 b(ak)g(a)308
b(\267)-542 b(sifrirana)374 b(p)34 b(oruk)-67 b(a)373
b(k)-34 b(o)67 b(ja)375 b(sadr)-34 b(\267)-572 b(zi)7749
16214 y FG(n)403 b FO(i)h(k)-34 b(o)67 b(ju)405 b(bi)f
FG(a)g FO(u)h(budu)-34 b(\266)-572 b(cnosti)406 b(mogao)e(p)34
b(oslati)404 b(mogu)-34 b(\266)-572 b(ci)404 b(izv)-34
b(or)404 b(te)g(soli.)9631 19225 y(Sljede)-34 b(\266)-572
b(ci)546 b(o)34 b(dnosi)547 b(\(tablica)g(6.2\))g(op)34
b(et)547 b(vrlo)e(priro)34 b(dno)547 b(o)34 b(dra)-34
b(\267)-572 b(za)-34 b(v)-67 b(a)67 b(ju)547 b(seman)-34
b(tiku)7749 20730 y(predik)-67 b(ata.)7883 21930 y(\267)7749
22236 y(Cinjenica)297 b(da)f(je)h FG(a)f FO(de)-64 b(\267)-542
b(sifrirao)296 b(p)34 b(oruku)297 b(sv)-67 b(ak)g(ak)-34
b(o)295 b(implicira)h(da)g(on)h(zna)g(tu)g(enkrip)34
b(ciju,)7749 23741 y(k)-67 b(ao)320 b(\267)-542 b(sto)386
b(zna)f(i)g(njen)h(sadr)-34 b(\267)-572 b(za)67 b(j)385
b(\()p FL(DEC)25087 23923 y Fj(1)26070 23741 y FO(i)g
FL(DEC)29784 23923 y Fj(2)30381 23741 y FO(\).)532 b(Ak)-34
b(o)386 b(zna)f(sparen)-34 b(u)386 b(p)34 b(oruku)385
b(zna)h(i)7749 25247 y(njene)404 b(djelo)-34 b(v)g(e)405
b(\()p FL(K)16552 25429 y Fj(1)17150 25247 y FO(\).)7749
26752 y(Aksiom)439 b FL(SR)-39 b(C)440 b FO(je)g(osno)-34
b(v)-67 b(a)440 b(rasu)p 23185 26139 V(div)-67 b(anja)440
b(o)f(izv)-34 b(oru)440 b(soli:)609 b(ak)-34 b(o)439
b(netk)-34 b(o)440 b(tk)-34 b(o)440 b(nije)g FG(a)f FO(zna)7749
28258 y(sol)404 b(k)-34 b(o)67 b(ju)405 b(je)f FG(a)g
FO(kreirao)f(i)g(p)34 b(oslao)340 b(\267)-542 b(sifriran)-34
b(u,)405 b(tada)g(je)f(netk)-34 b(o)405 b(to)f(morao)g(de)-64
b(\267)-542 b(sifrirati.)7749 29763 y(Aksiom)438 b FL(SEC)g
FO(o)34 b(dra)-34 b(\267)-572 b(za)-34 b(v)-67 b(a)438
b(sv)-34 b(o)67 b(jstv)-34 b(o)440 b(ta)67 b(jnosti)440
b(protok)-34 b(ola,)448 b(za)438 b(k)-34 b(o)67 b(je)439
b(je)f(dok)-67 b(azano)439 b(da)7749 31269 y(vrijedi)338
b(u)h(mo)34 b(delu)339 b(ra)-34 b(\267)-572 b(cuna)339
b(pro)34 b(cesa)338 b(\(lema)h(12\);)361 b(p)34 b(o)-64
b(\267)-542 b(steni)339 b(sudionik)g(mo)-34 b(\267)-572
b(ze)339 b(de)-64 b(\267)-542 b(sifrirati)7749 32774
y(samo)404 b(s)g(vlastitim)g(priv)-67 b(atnim)404 b(klju)-34
b(\267)-572 b(cem.)8946 36944 y FL(DEC)11938 37126 y
Fj(1)13732 36944 y FN(Decrypts)p FO(\()p FG(a;)202 b
FI(f)p FG(m)p FI(g)22114 37141 y FF(k)22683 36944 y FO(\))337
b FI(\241)-202 b(!)336 b FN(Kno)-34 b(ws)q FO(\()p FG(a;)202
b FI(f)p FG(m)p FI(g)33041 37141 y FF(k)33610 36944 y
FO(\))8946 38781 y FL(DEC)11938 38963 y Fj(2)13732 38781
y FN(Decrypts)p FO(\()p FG(a;)g FI(f)p FG(m)p FI(g)22114
38978 y FF(k)22683 38781 y FO(\))337 b FI(\241)-202 b(!)336
b FN(Kno)-34 b(ws)q FO(\()p FG(a;)202 b(m)p FO(\))8946
40619 y FL(K)10039 40801 y Fj(1)13732 40619 y FN(Kno)-34
b(ws)p FO(\()p FG(a;)202 b FO(\()p FG(x)19880 40801 y
FB(1)20406 40619 y FG(;)g(x)21638 40801 y FB(2)22163
40619 y FO(\)\))338 b FI(\241)-202 b(!)337 b FN(Kno)-34
b(ws)p FO(\()p FG(a;)202 b(x)31410 40801 y FB(1)31935
40619 y FO(\))270 b FI(^)f FN(Kno)-34 b(ws)q FO(\()p
FG(a;)202 b(x)39431 40801 y FB(2)39956 40619 y FO(\))8946
42456 y FL(SR)-39 b(C)1999 b FN(Source)p FO(\()p FG(n;)202
b(a;)g(t;)g(k)38 b FO(\))269 b FI(^)g FN(Kno)-34 b(ws)q
FO(\()p FG(b;)202 b(n)p FO(\))269 b FI(^)h FG(b)337 b
FI(6)p FO(=)f FG(a)g FI(\241)-202 b(!)337 b(9)202 b FG(c)p
FN(Decrypts)p FO(\()p FG(c;)g FI(f)p FG(t)p FI(g)45363
42653 y FF(k)45931 42456 y FO(\))8946 44294 y FL(SEC)2089
b FN(Honest)o FO(\()p FG(a)p FO(\))270 b FI(^)f FN(Decrypts)p
FO(\()p FG(b;)202 b FI(f)p FG(m)p FI(g)28455 44476 y
FF(a)29011 44294 y FO(\))337 b FI(\241)-202 b(!)336 b
FG(b)h FO(=)g FG(a)17467 48124 y FO(T)-101 b(ablica)404
b(6.2:)538 b(Odnosi)405 b(me)p 30092 47510 V(du)f(predik)-67
b(atima)9631 50840 y(Prv)g(a)404 b(tri)h(pra)-34 b(vila)404
b(naslje)p 21511 50226 V(div)-67 b(anja)406 b(dana)g(u)g(tablici)e(6.3)
h(demonstrira)67 b(ju)407 b(mo)34 b(dalna)7749 52345
y(sv)-34 b(o)67 b(jstv)-67 b(a)478 b([)p FG(Q)p FO(])14114
52542 y FF(b)14773 52345 y FG(\301)p FO(.)759 b(Preostala)444
b(\267)-572 b(cetiri)476 b(pra)-34 b(vila)477 b(p)34
b(ok)-67 b(azuju)477 b(da)h(su)g(sv)-34 b(o)67 b(jstv)-67
b(a)478 b(predik)-67 b(ata)7749 53851 y FN(Kno)-34 b(ws)p
FO(,)386 b FN(Sent)d FO(i)f FN(Decrypt)g FO(zadr)-34
b(\267)-572 b(zana)383 b(nak)-34 b(on)383 b(proizv)-34
b(oljne)382 b(ak)-34 b(cije;)389 b(ak)-34 b(o)383 b(je)f(netk)-34
b(o)383 b(znao,)7749 55356 y(de)-64 b(\267)-542 b(sifrirao,)357
b(ili)346 b(p)34 b(oslao)347 b(ne)-64 b(\267)-542 b(sto)347
b(dok)g(se)g(protok)-34 b(ol)347 b(izvr)-64 b(\267)-542
b(sa)-34 b(v)-67 b(ao,)357 b(tada)348 b(to)f(osta)67
b(je)314 b(\267)-572 b(cinjenica)7749 56862 y(te)404
b(runde,)g(b)34 b(ez)404 b(obzira)340 b(\267)-542 b(sto)404
b(ta)67 b(j)405 b(ili)e(drugi)i(agen)-34 b(ti)405 b(p)34
b(oslije)370 b(\267)-572 b(cinili.)7749 58367 y(Jedini)594
b(predik)-67 b(at)595 b(k)-34 b(o)67 b(ji)596 b(se)f(p)34
b(ona)-64 b(\267)-542 b(sa)595 b(druga)-34 b(\267)-572
b(cije)595 b(je)g FN(Source)p FO(.)1112 b(Nak)-34 b(on)532
b(\267)-542 b(sto)595 b FG(b)g FO(p)34 b(o)-64 b(\267)-542
b(salje)7749 59873 y(p)34 b(oruku)359 b(k)-34 b(o)67
b(ja)360 b(sadr)-34 b(\267)-572 b(zi)358 b FG(n)p FO(,)368
b(vi)-64 b(\267)-542 b(se)358 b(ne)h(mo)-34 b(\267)-572
b(zemo)358 b(tvrditi)h(da)h(je)f FI(f)p FG(t)p FI(g)36307
60070 y FF(k)36875 59873 y FO(,)368 b(k)-34 b(o)67 b(ju)296
b(\267)-542 b(salje)359 b FG(a)p FO(,)367 b(tv)-34 b(orac)7749
61378 y(soli)403 b FG(n)p FO(,)h(izv)-34 b(or)403 b(iz)g(k)-34
b(o)67 b(je)371 b(\266)-572 b(ce)404 b(drugi)g(agen)-34
b(ti)405 b(ev)-34 b(en)g(tualno)405 b(nau)-34 b(\267)-572
b(citi)404 b FG(n)p FO(.)9631 64389 y(Jedno)392 b(pra)-34
b(vilo)393 b(moramo)f(promatrati)h(o)34 b(dv)-34 b(o)67
b(jeno)394 b(o)34 b(d)393 b(ostalih,)h(s)f(vi)-64 b(\267)-542
b(se)392 b(p)34 b(osv)-34 b(e)g(\266)-572 b(cene)7749
65894 y(pa)-34 b(\267)-572 b(znje:)494 b(radi)316 b(se)f(o)g
FK(pr)-62 b(avilu)350 b(p)-62 b(o)g(\267)-558 b(stenja)p
FO(.)506 b(Ideja)316 b(sv)-34 b(o)67 b(jstv)-67 b(a)316
b('biti)f(p)34 b(o)-64 b(\267)-542 b(sten')316 b(je)f(v)-34
b(e)g(\266)-572 b(c)315 b(p)34 b(oznata,)7749 67400 y(p)g(o)-64
b(\267)-542 b(stenje)357 b(agen)-34 b(ta)358 b(zna)-34
b(\267)-572 b(ci)356 b(da)h(agen)-34 b(t)357 b(slijedi)f(pra)-34
b(vila)356 b(k)-34 b(o)67 b(je)357 b(propisuje)h(protok)-34
b(ol)357 b(u)g(svim)7749 68905 y(sesijama)526 b(u)h(k)-34
b(o)67 b(jima)527 b(je)f(sudjelo)-34 b(v)-67 b(ao)527
b(u)g(danom)g(prostoru)g(struna.)906 b(P)-34 b(o)-64
b(\267)-542 b(steni)527 b(agen)-34 b(t)7749 70411 y(izvr)-64
b(\267)-542 b(sa)-34 b(v)-67 b(a)499 b(to)-34 b(\267)-572
b(cno)501 b(ak)-34 b(cije)500 b(dane)h(rolama)f(protok)-34
b(ola.)827 b(U)501 b(slu)-34 b(\267)-572 b(ca)67 b(ju)501
b(da)g(je)f(Bob)h(p)34 b(o)-64 b(\267)-542 b(sten)7749
71916 y(agen)-34 b(t,)525 b(Alice)500 b(zna)g(k)-67 b(akvu)500
b(p)34 b(oruku)501 b(treba)g(o)-34 b(\267)-572 b(cekiv)-67
b(ati)499 b(k)-67 b(ao)500 b(o)34 b(dgo)-34 b(v)g(or)501
b(na)h(njen)f(p)34 b(oziv)27068 74956 y(80)p eop end
end
%%Page: 81 81
TeXDict begin HPSdict begin 81 80 bop 2435 9506 a Fy(Generi)-31
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b(pra)-31 b(vila)5283 14709 y Fe(G)6209 14820 y Fd(1)7689
13912 y Fy([)p Fw(Q)p Fy(])9178 14078 y Fv(A)9900 13912
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Fw(Q)p Fy(])10068 15672 y Fv(a)10605 15506 y Fy(\()p
Fw(\301)246 b Ft(^)g Fw(\303)40 b Fy(\))18818 14709 y
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14078 y Fv(a)23249 13912 y Fw(\301)1660 b(\301)307 b
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13973 y Fw(\301)p 34774 14454 4532 45 v 35604 15506 a
Fy([)p Fw(Q)p Fy(])37093 15672 y Fv(A)37815 15506 y Fw(\301)2435
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b(anja)5257 25185 y Fe(P)6062 25296 y Fd(1)8458 24388
y Fy([)p Fw(Q)p Fy(])9947 24554 y Fv(b)10393 24388 y
Fx(P)-31 b(ersist)q Fy(\()p Fw(a;)184 b(t)p Fy(\))p 6711
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Ft(i)p Fy(])10862 26148 y Fv(b)11309 25982 y Fx(P)-31
b(ersist)r Fy(\()p Fw(a;)184 b(t)p Fy(\))22806 25185
y Fe(P)23611 25296 y Fd(2)25837 24388 y Fy([)p Fw(Q)p
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v 25090 25982 a([)p Fw(Q)p Fy(\()p Fw(x)p Fy(\)])28072
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Fd(3)8597 27532 y Fy([)p Fw(Q)p Fy(])10086 27698 y Fv(b)10532
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Fw(Q)p Fy(])28600 27698 y Fv(b)29046 27532 y Fx(P)-31
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Fy(\()p Fw(x)p Fy(\)\)])30619 29292 y Fv(b)31066 29126
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31473 y Fe(P)6062 31584 y Fd(5)8458 30676 y Fy([)p Fw(Q)p
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32436 y Fv(b)11309 32270 y Fx(Source)q Fy(\()p Fw(n;)184
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y Fd(6)25837 30676 y Fy([)p Fw(Q)p Fy(])27326 30842 y
Fv(b)27772 30676 y Fx(Source)q Fy(\()p Fw(n;)184 b(a;)g(t;)g(k)35
b Fy(\))p 24260 31218 12789 45 v 25090 32270 a([)p Fw(Q)p
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eop end end
%%Page: 82 82
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eop end end
%%Page: 83 83
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%%Page: 84 84
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