(original) (raw)

%!PS-Adobe-2.0 %%Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: ex4.dvi %%CreationDate: Sun May 04 08:59:00 2008 %%Pages: 2 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMBX10 CMR10 CMR12 CMTI10 CMMI10 CMSY10 CMR8 CMMI8 CMR6 %%+ CMSY8 CMMI6 CMBXTI10 CMCSC10 CMEX10 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe -P cmz -t letter ex4 %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2008.05.04:0858 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro %! 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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 83 /S put dup 97 /a put dup 116 /t 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. 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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 58 /colon put dup 67 /C put dup 83 /S put dup 100 /d put dup 101 /e put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p 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 D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 110 /n put dup 113 /q put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 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 0 /minus put dup 48 /prime put dup 102 /braceleft put dup 103 /braceright put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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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 49 /one put dup 50 /two put dup 51 /three put dup 103 /g put dup 108 /l put dup 111 /o put dup 112 /p put dup 121 /y put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 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 34 /epsilon put dup 59 /comma put dup 79 /O put dup 84 /T put dup 99 /c put dup 105 /i put dup 107 /k put dup 110 /n put dup 113 /q put dup 115 /s put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 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 6 /Sigma put dup 40 /parenleft put dup 41 /parenright put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 103 /g put dup 108 /l put dup 111 /o put dup 112 /p put dup 121 /y put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 10 /circlemultiply put dup 15 /bullet put dup 18 /reflexsubset put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 50 /element put dup 54 /negationslash put dup 65 /A 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 125 /diamond put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 14 /delta put dup 21 /lambda put dup 25 /pi put dup 34 /epsilon put dup 58 /period put dup 59 /comma put dup 62 /greater put dup 67 /C put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H 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 83 /S put dup 84 /T put dup 86 /V 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 105 /i put dup 108 /l put dup 110 /n put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-32 -250 1048 750}readonly def 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 12 /fi put dup 14 /ffi put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 56 /eight put dup 58 /colon put dup 59 /semicolon put dup 66 /B put dup 68 /D put dup 73 /I put dup 76 /L put dup 77 /M put dup 84 /T 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 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 46 /period put dup 52 /four put dup 69 /E put dup 99 /c put dup 101 /e put dup 105 /i put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 120 /x put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 1 /Delta put dup 6 /Sigma put dup 10 /Omega put dup 12 /fi put dup 14 /ffi 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 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 56 /eight put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 80 /P put dup 81 /Q put dup 83 /S put dup 84 /T put dup 85 /U put dup 89 /Y put dup 91 /bracketleft put dup 93 /bracketright 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 readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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9AF956D0A0CAC3E7889A4998EE8564F048DF55451DF5721C96175AE46B30C26B 10A12CE9E61A3652632C6787B8C3FBA85227A8F0B9D1468873ADEAC8B3E93D9F 2F33919FEBB9C9B0169FAF78B72B48ACBFA39688DFE4CA4300CCF0CD56D9BA2B 5E622EE570AEA2B489ADAD886C32EF521316113F062FA0192E704F0E26640CF7 640B5507F131340F2E1D6B40035CF929AD626319233046AA76152FB1A0425066 C09C26D295ABE99A535867A22B722C8BA42594CB3A881C7CDCCD49D549BFAC81 0C4D4DDDFE42 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 12 /fi put dup 14 /ffi put dup 40 /parenleft put dup 41 /parenright put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 58 /colon put dup 65 /A put dup 67 /C put dup 69 /E put dup 73 /I put dup 76 /L put dup 77 /M put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T 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 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 120 /x put dup 121 /y put dup 122 /z 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b(v)m(eri\014er)e(that)h(giv)m(en)g(oracle)h (access)f(to)g Fj(q)i Fm(strings)d Fj(y)2604 3323 y Fh(1)2643 3309 y Fj(;)15 b(:)g(:)g(:)i(;)e(y)2890 3323 y Fg(q)2969 3309 y Fm(and)40 b(to)i(a)g(pro)s(of)e Fj(\031)s Fm(,)k(uses)377 3422 y(randomness)29 b Fj(r)s Fm(,)i(mak)m(es)g Fj(q)1290 3389 y Fe(0)1343 3422 y Fm(queries)g(to)g Fj(y)1806 3436 y Fh(1)1845 3422 y Fj(;)15 b(:)g(:)g(:)h(;)f(y)2091 3436 y Fg(q)2160 3422 y Fm(and)29 b Fj(\031)s Fm(,)i(and)f(ac)m(hiev)m(es)i (the)f(follo)m(wing:)486 3609 y Fi(\017)46 b Fn(Completeness:)36 b Fm(If)19 b Fj(y)1394 3623 y Fh(1)1433 3609 y Fj(;)c(:)g(:)g(:)i(;)e (y)1680 3623 y Fg(q)1738 3609 y Fm(are,)23 b(resp)s(ectiv)m(ely)-8 b(,)25 b(the)20 b(lo)m(w)h(degree)g(extensions)g(of)f Fj(x)3559 3623 y Fh(1)3599 3609 y Fj(;)15 b(:)g(:)g(:)h(;)f(x)3852 3623 y Fg(q)3916 3609 y Fi(2)577 3722 y(f)q Fm(0)p Fj(;)g Fm(1)p Fi(g)799 3680 y Fg(n)846 3722 y Fm(,)27 b(and)f Fj(T)13 b Fm(\()p Fj(x)1224 3736 y Fh(1)1263 3722 y Fj(;)i(:)g(:)g(:)i (;)e(x)1517 3736 y Fg(q)1555 3722 y Fm(\))26 b(=)f Fj(tr)s(ue)p Fm(,)h(then)g(there)g(exists)g(a)g(pro)s(of)f Fj(\031)k Fm(that)d(the)g(v)m(eri\014er)g(alw)m(a)m(ys)577 3835 y(accepts.)486 3981 y Fi(\017)46 b Fn(Soundness:)k Fm(If)34 b(either)h(\(i\))h(there)f(is)f Fj(i)f Fi(2)f Fm([)p Fj(q)s Fm(])j(suc)m(h)f(that)h Fj(y)2689 3995 y Fg(i)2752 3981 y Fm(is)f(0)p Fj(:)p Fm(2-far)i(from)e(b)s(eing)g(the)h(lo)m(w)577 4094 y(degree)h(extension)f(of)g(some)h Fj(x)1664 4108 y Fg(i)1724 4094 y Fi(2)d(f)p Fm(0)p Fj(;)15 b Fm(1)p Fi(g)2040 4052 y Fg(n)2087 4094 y Fm(;)37 b(or)e(\(ii\))h(for)e(eac)m (h)i Fj(i)d Fi(2)g Fm([)p Fj(q)s Fm(],)j Fj(y)3131 4108 y Fg(i)3194 4094 y Fm(is)f(0)p Fj(:)p Fm(8-close)i(to)f(the)577 4207 y(lo)m(w)g(degree)f(extension)g(of)g(some)g Fj(x)1831 4221 y Fg(i)1892 4207 y Fi(2)d(f)p Fm(0)p Fj(;)15 b Fm(1)p Fi(g)2207 4165 y Fg(n)2254 4207 y Fm(,)36 b Fk(but)e Fj(T)13 b Fm(\()p Fj(x)2623 4221 y Fh(1)2663 4207 y Fj(;)i(:)g(:)g(:)h (;)f(x)2916 4221 y Fg(q)2955 4207 y Fm(\))33 b(=)f Fj(f)10 b(al)r(se)p Fm(;)36 b(then)e(for)h(an)m(y)577 4320 y(pro)s(of)30 b Fj(\031)s Fm(,)h(the)f(v)m(eri\014er)h(rejects)g(with)f(some)h (constan)m(t)g(probabilit)m(y)-8 b(.)416 4533 y(\(a\))46 b Fn(Inner)35 b(v)m(eri\014er.)43 b Fm(Based)31 b(on)g(Theorem)f(1,)i (sho)m(w)f(that)g(an)m(y)g(e\016cien)m(tly)i(decidable)e(predicate)577 4645 y Fj(T)43 b Fm(on)31 b Fj(q)i(n)p Fm(-bit)d(strings)g(has)g(a)h (\()p Fj(O)s Fm(\()p Fj(q)19 b Fm(log)e Fj(n)p Fm(\))p Fj(;)e(O)s Fm(\()p Fj(q)s Fm(\)\))2317 4678 y Fe(f)r Fh(0)p Fg(;)p Fh(1)p Fe(g)2479 4648 y Ff(p)r(oly)c(log)h Fd(q)r(n)2772 4645 y Fm(-restricted)32 b(inner)d(v)m(eri\014er.)411 4804 y(\(b\))45 b Fn(Comp)s(osition)36 b(Theorem.)k Fm(Pro)m(v)m(e)32 b(the)e(follo)m(wing)i(comp)s(osition)f(theorem:)656 4950 y Fi(\017)46 b Fm(Let)39 b Fj(V)971 4964 y Fh(1)1050 4950 y Fm(b)s(e)f(a)h(\()p Fj(r)m(;)15 b(q)s Fm(\))1458 4964 y Fh(\006)1509 4973 y Ff(1)1549 4950 y Fm(-restricted)39 b(v)m(eri\014er)g(for)g Fb(Sa)-6 b(t)p Fm(.)64 b(Assume)39 b(that)g(the)g(test)g(that)h Fj(V)3861 4964 y Fh(1)747 5063 y Fm(p)s(erforms)f(on)i(its)g Fj(q)i Fm(queries)e(is)f(giv)m(en)i (b)m(y)e(the)h(e\016cien)m(tly)h(decidable)f Fj(q)s Fm(-ary)g (predicate)747 5176 y Fj(T)13 b Fm(,)48 b(where)43 b(the)i(answ)m(ers)e (to)i(the)f Fj(q)j Fm(queries)d(are)h(giv)m(en)g(as)f(binary)f(strings) h(of)h(length)747 5289 y Fj(n)802 5256 y Fe(0)850 5289 y Fm(=)25 b Fi(d)p Fm(log)18 b Fi(j)q Fm(\006)1211 5303 y Fh(1)1250 5289 y Fi(je)p Fm(.)656 5419 y Fi(\017)46 b Fm(Let)31 b Fj(V)963 5433 y Fh(2)1033 5419 y Fm(b)s(e)f(a)g(\()p Fj(r)1311 5386 y Fe(0)1335 5419 y Fj(;)15 b(q)1419 5386 y Fe(0)1442 5419 y Fm(\))1477 5433 y Fh(\006)1528 5442 y Ff(2)1567 5419 y Fm(-restricted)32 b(inner)d(v)m(eri\014er)i(for)f Fj(T)13 b Fm(.)1927 5716 y(1)p eop end %%Page: 2 2 TeXDict begin 2 1 bop 577 159 a Fm(Then,)28 b(there)h(is)g(a)g(\()p Fj(r)19 b Fm(+)d Fj(r)1459 126 y Fe(0)1482 159 y Fj(;)f(q)1566 126 y Fe(0)1590 159 y Fm(\))1625 173 y Fh(\006)1676 182 y Ff(2)1715 159 y Fm(-restricted)29 b(v)m(eri\014er)g Fj(V)49 b Fm(for)28 b Fb(Sa)-6 b(t)p Fm(.)39 b(If)28 b Fj(V)3055 173 y Fh(1)3123 159 y Fm(and)g Fj(V)3351 173 y Fh(2)3419 159 y Fm(ha)m(v)m(e)i(p)s(erfect)577 271 y(completeness,)g(then)f(so)f(do)s(es)g Fj(V)21 b Fm(.)40 b(If)27 b Fj(V)1945 285 y Fh(1)2013 271 y Fm(has)h(soundness)f Fj(s)2640 285 y Fh(1)2708 271 y Fm(and)g Fj(V)2935 285 y Fh(2)3003 271 y Fm(has)h(soundness)f Fj(s)3630 285 y Fh(2)3669 271 y Fm(,)i(then)577 384 y Fj(V)51 b Fm(has)30 b(soundness)f Fj(s)1312 398 y Fh(1)1371 384 y Fm(+)20 b Fj(s)1505 398 y Fh(2)1544 384 y Fm(.)261 597 y(3.)85 b(\(a\))46 b Fn(The)35 b(Expander)g(Mixing)h(Lemma.)41 b Fm(Let)31 b Fj(G)26 b Fm(=)g(\()p Fj(V)5 b(;)15 b(E)5 b Fm(\))32 b(b)s(e)e(an)g(\()p Fj(n;)15 b(d;)g(\025)p Fm(\)-expander.)43 b(Pro)m(v)m(e)577 710 y(that)31 b(for)f(an)m(y)h Fj(S;)15 b(T)38 b Fi(\022)25 b Fj(V)c Fm(,)1580 827 y Fa(\014)1580 882 y(\014)1580 936 y(\014)1580 991 y(\014)1610 959 y Fj(E)5 b Fm(\()p Fj(S;)15 b(T)e Fm(\))22 b Fi(\000)d(j)q Fj(S)5 b Fi(j)15 b(j)p Fj(T)e Fi(j)2298 897 y Fj(d)p 2294 938 55 4 v 2294 1021 a(n)2359 827 y Fa(\014)2359 882 y(\014)2359 936 y(\014)2359 991 y(\014)2415 959 y Fi(\024)25 b Fj(\025)2564 877 y Fa(p)p 2654 877 243 4 v 2654 959 a Fi(j)q Fj(S)5 b Fi(j)15 b(j)p Fj(T)e Fi(j)411 1230 y Fm(\(b\))45 b Fn(Randomness-e\016cien)m(t)37 b(ampli\014cation.) j Fm(Sho)m(w)30 b(that)h(for)f(an)m(y)h Fj(r)i Fm(and)d Fj(")25 b(>)g Fm(0,)1447 1472 y Fj(P)13 b(C)7 b(P)1658 1473 y Ff(2)p 1658 1485 31 3 v 1658 1526 a(3)1699 1500 y Fg(;)1729 1473 y Ff(1)p 1728 1485 V 1728 1526 a(3)1773 1472 y Fm([)p Fj(r)m(;)15 b(O)s Fm(\(1\)])27 b Fi(\022)e Fj(P)13 b(C)7 b(P)2412 1486 y Fh(1)p Fe(\000)p Fg(";")2591 1472 y Fm([)p Fj(r)m(;)15 b Fm(p)s(oly)r(\()2913 1411 y(1)p 2913 1451 46 4 v 2915 1534 a Fj(")2969 1472 y Fm(\)])261 1740 y(4.)46 b Fn(Robustization.)c Fm(Sho)m(w)29 b(that)h(an)m(y)g (language)h Fj(L)25 b Fi(2)g Fj(P)13 b(C)7 b(P)2440 1754 y Fg(c;s)2527 1740 y Fm([)p Fj(r)m(;)15 b(q)s Fm(])2699 1754 y Fh(\006)2785 1740 y Fm(has)29 b(a)h Fj(P)13 b(C)7 b(P)43 b Fm(v)m(eri\014er)29 b(with)h(the)377 1853 y(same)g (completeness)h Fj(c)p Fm(,)g(soundness)d Fj(s)h Fm(and)g(randomness)g Fj(r)j Fm(that)e(mak)m(es)h Fj(q)3000 1820 y Fe(0)3048 1853 y Fm(=)25 b Fj(O)s Fm(\()p Fj(q)18 b Fm(log)g Fi(j)p Fm(\006)p Fi(j)p Fm(\))30 b(queries)377 1965 y(to)h(a)g(binary)f(pro)s (of)f(and)h(has)g(robust)g(soundness)f Fj(\016)g Fm(=)c(\012\()2412 1930 y Fh(1)p 2412 1945 36 4 v 2413 1997 a Fg(q)2457 1965 y Fm(\).)377 2116 y(Hin)m(t:)67 b(Use)44 b(the)f(existence)h(of)g (explicit)g(co)s(des)f(with)g(constan)m(t)i(rate)e(and)g(linear)g (distance,)48 b(i.e.,)377 2229 y(functions)33 b Fj(E)839 2244 y Fg(k)911 2229 y Fm(:)c Fi(f)q Fm(0)p Fj(;)15 b Fm(1)p Fi(g)1188 2187 y Fg(k)1260 2229 y Fi(!)29 b(f)p Fm(0)p Fj(;)15 b Fm(1)p Fi(g)1602 2187 y Fg(O)r Fh(\()p Fg(k)r Fh(\))1788 2229 y Fm(suc)m(h)33 b(that)g(for)g(ev)m(ery)g(t)m(w) m(o)h Fj(x)c Fi(6)p Fm(=)f Fj(y)j Fi(2)d(f)p Fm(0)p Fj(;)15 b Fm(1)p Fi(g)3324 2187 y Fg(k)3400 2229 y Fm(it)33 b(holds)f(that)377 2342 y(\001\()p Fj(E)555 2357 y Fg(k)598 2342 y Fm(\()p Fj(x)p Fm(\))p Fj(;)15 b(E)827 2357 y Fg(k)871 2342 y Fm(\()p Fj(y)s Fm(\)\))26 b Fi(\025)1156 2306 y Fh(1)p 1156 2321 V 1156 2373 a(3)1201 2342 y Fm(.)261 2529 y(5.)46 b Fn(Quadratic)35 b(testing.)40 b Fm(Pro)m(v)m(e)32 b(the)e(follo)m (wing)i(claims:)416 2717 y(\(a\))46 b Fn(T)-9 b(ensor)25 b(pro)s(duct.)37 b Fm(F)-8 b(or)22 b(an)m(y)f(four)f(v)m(ectors)i Fj(a;)15 b(b;)g(x;)g(y)29 b Fi(2)c(f)q Fm(0)p Fj(;)15 b Fm(1)p Fi(g)2770 2675 y Fg(n)2816 2717 y Fm(,)23 b(it)f(holds)e(that) h Fi(h)p Fj(a)q Fi(\012)q Fj(b;)15 b(x)q Fi(\012)q Fj(y)s Fi(i)25 b Fm(=)577 2830 y Fi(h)p Fj(a;)15 b(x)p Fi(i)22 b(\001)e(h)p Fj(b;)15 b(y)s Fi(i)p Fm(.)411 2976 y(\(b\))45 b Fn(Lemma.)f Fm(F)-8 b(or)33 b(an)m(y)f Fj(n)20 b Fi(\002)h Fj(n)31 b Fm(non-zero)h(matrix)g Fj(M)42 b Fm(o)m(v)m(er)33 b(the)f(\014eld)f Fi(f)q Fm(0)p Fj(;)15 b Fm(1)p Fi(g)q Fm(,)33 b(when)d(pic)m(king)j(t)m(w)m(o)577 3089 y(v)m(ectors)f Fj(x;)15 b(y)29 b Fi(2)24 b(f)q Fm(0)p Fj(;)15 b Fm(1)p Fi(g)1360 3047 y Fg(n)1437 3089 y Fm(uniformly)29 b(at)i(random,)f (with)g(probabilit)m(y)h(at)g(most)3337 3053 y Fh(3)p 3337 3068 V 3337 3120 a(4)3382 3089 y Fm(,)g Fj(x)3490 3056 y Fg(T)3545 3089 y Fj(M)10 b(y)28 b Fm(=)d(0.)421 3246 y(\(c\))46 b Fn(Quadratic)23 b(testing.)37 b Fm(The)20 b(quadratic)g(functions)g(enco)s(ding)h(is)f(a)g(mapping)g Fj(QF)38 b Fm(:)26 b Fi(f)p Fm(0)p Fj(;)15 b Fm(1)p Fi(g)3710 3204 y Fg(n)p Fe(\000)p Fh(1)3872 3246 y Fi(!)577 3396 y(f)q Fm(0)p Fj(;)g Fm(1)p Fi(g)799 3354 y Fh(2)834 3330 y Fd(n)872 3309 y Ff(2)946 3396 y Fm(that)30 b(maps)f(\()p Fj(a)1462 3410 y Fh(2)1502 3396 y Fj(;)15 b(:)g(:)g(:)h(;)f(a)1751 3410 y Fg(n)1799 3396 y Fm(\))25 b Fi(2)g(f)q Fm(0)p Fj(;)15 b Fm(1)p Fi(g)2168 3354 y Fg(n)p Fe(\000)p Fh(1)2334 3396 y Fm(to)31 b Fj(H)7 b Fm(\()p Fj(a)2611 3363 y Fe(0)2653 3396 y Fi(\012)19 b Fj(a)2791 3363 y Fe(0)2814 3396 y Fm(\),)30 b(where)f Fj(a)3214 3363 y Fe(0)3263 3396 y Fm(=)c(\(1)p Fj(;)15 b(a)3527 3410 y Fh(2)3568 3396 y Fj(;)g(:)g(:)g(:)h(;)f(a)3817 3410 y Fg(n)3865 3396 y Fm(\))577 3509 y(and)26 b Fj(H)32 b Fm(is)26 b(the)g(Hadamard)g(enco)s (ding.)39 b(Sho)m(w)26 b(that)g Fj(QF)39 b Fm(is)26 b(lo)s(cally)h (testable,)i(i.e.,)f(there)e(exists)577 3653 y(a)j(randomized)f(pro)s (cedure)f Fi(A)h Fm(that)h(giv)m(en)g(a)g(w)m(ord)e Fj(w)h Fi(2)d(f)q Fm(0)p Fj(;)15 b Fm(1)p Fi(g)2787 3611 y Fh(2)2822 3588 y Fd(n)2860 3567 y Ff(2)2932 3653 y Fm(mak)m(es)29 b Fj(O)s Fm(\(1\))g(queries)f(to)h Fj(w)577 3766 y Fm(to)i(decide)g (whether)f Fj(w)j Fm(is)d(close)i(to)f(a)g Fj(QF)43 b Fm(co)s(dew)m(ord:)656 3912 y Fi(\017)j Fn(Completeness:)41 b Fm(If)30 b Fj(w)d Fm(=)e Fj(QF)13 b Fm(\()p Fj(a)p Fm(\))31 b(for)g(some)f Fj(a)c Fi(2)e(f)q Fm(0)p Fj(;)15 b Fm(1)p Fi(g)2764 3870 y Fg(n)p Fe(\000)p Fh(1)2901 3912 y Fm(,)30 b(then)g Fi(A)g Fm(alw)m(a)m(ys)i(accepts.)656 4041 y Fi(\017)46 b Fn(Soundness:)40 b Fm(If)28 b(for)f(ev)m(ery)h Fj(a)e Fi(2)f(f)p Fm(0)p Fj(;)15 b Fm(1)p Fi(g)2132 4000 y Fg(n)p Fe(\000)p Fh(1)2269 4041 y Fm(,)28 b Fj(dist)p Fm(\()p Fj(w)r(;)15 b(QF)e Fm(\()p Fj(a)p Fm(\)\))28 b Fi(\025)d Fj(\016)s Fm(,)k(then)f Fi(A)f Fm(rejects)h(with)747 4154 y(probabilit)m(y)j(at)g(least)h(\012\()p Fj(\016)s Fm(\).)261 4342 y Fi(})45 b Fn(The)23 b(PCP)h(Theorem.)37 b Fk(Bonus)24 b(question)f(\(20)i(p)-5 b(oints\):)37 b Fm(Pro)m(v)m(e)21 b(that)g Fj(N)10 b(P)38 b Fi(\022)25 b Fj(P)13 b(C)7 b(P)3313 4370 y Fh(1)p Fg(;)3378 4343 y Ff(1)p 3378 4355 31 3 v 3378 4396 a(2)3422 4342 y Fm([)p Fj(O)s Fm(\(log)18 b Fj(n)p Fm(\))p Fj(;)d(O)s Fm(\(1\)].)377 4467 y(Y)-8 b(ou)38 b(ma)m(y)h(use)e(the)h(comp)s(osition)g(theorem)g (w)m(e)g(sa)m(w)g(in)f(class)i(or)e(the)h(Arora-Safra)g(comp)s(osition) 377 4580 y(from)30 b(Question)h(2.)1927 5416 y(2)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF