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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 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 100 /d put dup 105 /i put dup 107 /k put readonly def /FontBBox{11 -250 1241 750}readonly 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 8 /braceleftbig put dup 9 /bracerightbig put dup 12 /vextendsingle put readonly def /FontBBox{-24 -2960 1454 772}readonly 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 /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 67 /C put readonly def /FontBBox{-59 -250 1235 750}readonly 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 3 /square put dup 64 /squareimage put readonly def /FontBBox{8 -463 1331 1003}readonly 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 3 /asteriskmath put dup 21 /greaterequal put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put readonly def /FontBBox{-30 -955 1185 779}readonly 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 78 /N put readonly def /FontBBox{-55 -420 2343 920}readonly 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 66 /B put dup 76 /L put dup 77 /M put dup 78 /N put dup 82 /R put dup 83 /S put dup 84 /T put dup 88 /X put dup 100 /d put dup 101 /e put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 114 /r put dup 115 /s put dup 120 /x put readonly def /FontBBox{-24 -250 1110 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 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0000000000000000000000000000000000000000000000000000000000000000 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 72 /H put dup 80 /P put readonly def /FontBBox{-20 -250 1193 750}readonly 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 0 /minus put dup 1 /periodcentered put dup 3 /asteriskmath put dup 15 /bullet put dup 17 /equivalence put dup 18 /reflexsubset put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 67 /C put dup 80 /P put dup 91 /union put dup 92 /intersection put dup 94 /logicaland put dup 95 /logicalor put dup 98 /floorleft put dup 99 /floorright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 118 /subsetsqequal put dup 121 /dagger put dup 122 /daggerdbl put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % 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 (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 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 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 21 /lambda put dup 26 /rho put dup 27 /sigma put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 82 /R put dup 83 /S put dup 88 /X put dup 90 /Z put dup 98 /b put dup 99 /c put dup 100 /d put dup 102 /f put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 111 /o put dup 113 /q put dup 114 /r put dup 115 /s put dup 117 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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 11 /ff put dup 12 /fi put dup 19 /acute put dup 39 /quoteright 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 51 /three put dup 52 /four put dup 53 /five put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 61 /equal put dup 65 /A put dup 67 /C put dup 68 /D put dup 70 /F put dup 72 /H put dup 73 /I put dup 74 /J 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 87 /W 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 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 currentdict end currentfile eexec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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 3 /asteriskmath put dup 121 /dagger put dup 122 /daggerdbl put readonly def /FontBBox{-15 -951 1252 782}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % 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 (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 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 11 /ff put dup 12 /fi 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 58 /colon 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 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 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 127 /dieresis put readonly def /FontBBox{-36 -251 1103 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 1 /Delta put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 19 /acute put dup 22 /macron put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign 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 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 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 92 /quotedblleft 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 dup 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 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0000000000000000000000000000000000000000000000000000000000000000 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 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 105 /i 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 dup 120 /x put readonly def /FontBBox{-163 -250 1146 969}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 1 /Delta 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 52 /four put dup 72 /H put dup 77 /M put dup 79 /O put dup 80 /P put dup 84 /T put dup 98 /b put dup 100 /d put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 111 /o put dup 112 /p put dup 116 /t put dup 119 /w put readonly def /FontBBox{-36 -250 1070 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 15 /epsilon1 put dup 61 /slash put dup 62 /greater put dup 82 /R put dup 83 /S put readonly def /FontBBox{-32 -250 1048 750}readonly 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 65 /A put dup 97 /a put dup 98 /b put dup 99 /c put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-301 -250 1164 946}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8B731A88D7740B0DDAED1B3F82 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8000 8000 (aaaa.dvi) @start /Fa 135[946 1[946 996 697 707 732 2[897 996 1[498 946 1[498 996 1[548 818 996 797 996 872 9[1852 2[1247 1[1338 3[1402 8[1177 2[1275 13[897 897 897 897 2[498 598 45[{}30 1594.02 /CMBX12 rf /Fb 207[243 48[{}1 664.176 /CMSY6 rf /Fc 148[439 1[296 4[427 100[{}3 664.176 /CMMI6 rf /Fd 243[443 2[775 775 8[{}3 1328.35 /CMEX10 rf /Fe 188[783 67[{}1 885.568 /CMBX8 rf /Ff 191[1033 60[1033 3[{}2 1328.35 /MSAM10 rf /Fg 205[627 941 255 14[941 11[732 17[470 2[732{}7 885.568 /CMSY8 rf /Fh 177[959 78[{}1 1328.35 /MSBM10 rf /Fi 134[789 1[1079 789 830 581 589 610 1[830 747 830 1245 415 789 1[415 830 747 457 682 830 664 1[726 12[1039 1[1115 1[1021 1[1168 1[898 7[1145 1079 1[1128 7[747 747 747 747 747 747 747 747 747 747 1[415 46[{}40 1328.35 /CMBX12 rf /Fj 135[530 4[435 425 3[571 832 1[490 381 320 3[436 484 11[774 3[548 572 709 3[747 904 640 9[710 66[{}18 885.568 /CMMI8 rf /Fk 175[544 7[595 21[406 406 49[{}4 664.176 /CMR6 rf /Fl 137[1033 11[369 517 517 664 664 2[590 590 2[886 886 1[886 886 10[924 12[699 10[738 0 0 3[886 1328 7[1328 1328 6[1328 11[1033 1033 1[1033 1033 1[664 13[369 1033{}29 1328.35 /CMSY10 rf /Fm 134[634 739 930 1[740 1[613 586 577 1[625 776 1138 1[676 538 444 2[641 1[676 560 553 7[890 1[1079 4[800 990 2[994 1042 1258 885 2[574 3[963 1080 931 988 975 2[1012 650 1012 361 361 30[739 671 4[759 5[525 576 675 734 827 11[{}44 1328.35 /CMMI12 rf /Fn 134[581 2[581 581 581 581 581 1[581 581 581 581 581 2[581 581 581 581 581 581 581 581 581 32[581 17[581 581 45[{}23 1106.96 /CMTT10 rf /Fo 134[584 584 799 584 615 430 437 434 584 615 553 615 922 307 2[307 615 553 338 492 615 492 615 553 11[830 1[615 815 1[753 1[830 1015 692 1[569 400 2[723 1[846 799 1[830 7[553 553 553 1[553 553 553 553 553 553 1[307 369 307 4[307 19[553 19[{}50 1106.96 /CMR10 rf /Fp 133[406 406 117[454 3[{}3 774.872 /CMSY7 rf /Fq 128[664 5[631 598 863 598 697 432 531 548 598 664 664 731 1063 332 598 1[399 664 598 399 598 664 598 598 664 6[797 5[930 731 948 996 881 996 966 1165 815 999 682 501 966 1005 848 881 981 930 914 966 6[399 6[664 664 664 664 1[399 465 399 31[731 797 11[{}56 1328.35 /CMTI12 rf /Fr 128[650 3[650 578 686 686 939 686 723 506 513 506 686 723 650 723 1084 361 686 397 361 723 650 397 578 723 578 723 650 3[361 650 361 795 975 975 1336 975 975 939 723 957 1[885 1012 975 1192 813 1011 668 469 975 1021 849 885 993 939 921 975 3[1012 1[361 361 650 650 650 650 650 650 650 650 650 650 650 361 434 361 1012 1[506 506 361 3[1084 650 361 10[650 2[650 4[1084 1[723 759 939 8[1084 1[{}87 1328.35 /CMR12 rf /Fs 135[1136 1[1136 1196 837 849 879 2[1076 1196 1793 598 2[598 2[658 982 1196 956 1[1046 11[1654 2[1605 3[1683 4[801 3[1412 1649 1554 1530 13[1076 1076 1076 1076 49[{}28 1912.83 /CMBX12 rf /Ft 135[562 1[558 651 403 496 511 2[620 681 991 310 2[372 1[558 1[558 620 558 558 620 97[{}17 1212.12 /CMTI10 rf /Fu 234[943 20[943{}2 1212.12 /CMSY10 rf /Fv 136[680 2[366 3[523 470 1[784 261 2[261 523 470 2[523 1[523 13[680 3[640 732 1[862 4[705 19[470 470 470 470 470 4[732 1[366 366 38[784 1[{}25 885.568 /CMR8 rf /Fw 172[743 920 19[943 606 45[492 15[{}5 1212.12 /CMMI10 rf /Fx 139[542 550 574 14[620 774 678 31[1054 65[{}7 1212.12 /CMBX10 rf /Fy 133[539 640 640 875 640 673 471 478 475 640 673 606 673 1010 337 640 1[337 673 606 370 539 673 539 673 606 9[1246 1[909 875 673 2[825 1[909 4[438 909 1[791 4[909 3[943 11[606 606 1[337 404 337 2[471 471 20[606 6[673 707 11[{}46 1212.12 /CMR10 rf /Fz 133[492 492 117[553 3[{}3 1106.96 /CMSY10 rf /FA 134[824 2[824 867 607 1[607 1[867 780 867 2[824 1[434 867 2[694 867 2[780 13[867 6[975 5[1019 1[1192 1[1105 66[{}19 1594.02 /CMR12 rf /FB 137[1363 1435 1004 1019 1055 2[1291 1435 2152 3[717 1[1291 1[1178 1435 1148 1[1256 12[1796 15[1980 1865 67[{}17 2295.84 /CMBX12 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 8000dpi TeXDict begin %%PaperSize: A4 end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 333 6697 a FB(Constructiv)-72 b(e)864 b(Dimension)e(and)e(T)-215 b(uring)862 b(Degrees)1930 10641 y FA(Lauren)-43 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b(tify)448 b(an)g(in\014nite)f(binary)g(sequence)h Fm(S)471 b Fl(2)392 b Fi(C)448 b Fr(with)g(the)f(language)i(of)f(whic)-36 b(h)0 46778 y Fm(S)491 b Fr(is)414 b(the)f(c)-36 b(haracteristic)414 b(sequence;)421 b(that)413 b(is,)419 b(the)413 b(set)g(that)h(con)-36 b(tains)413 b Fm(n)i Fr(exactly)g(when)e Fm(S)77 b Fr([)p Fm(n)p Fr(])370 b(=)f(1.)572 b(In)0 48383 y(suc)-36 b(h)464 b(a)i(case,)474 b(giv)-36 b(en)466 b Fm(x)423 b Fl(2)f(f)p Fr(0)p Fm(;)221 b Fr(1)p Fl(g)16343 47901 y Fg(\003)16870 48383 y Fr(,)474 b Fm(S)77 b Fr([)p Fm(x)p Fr(])466 b(ma)-36 b(y)466 b(also)g(b)36 b(e)465 b(in)-36 b(terpreted)463 b(as)j(the)f(binary)g(condition)g(\\)p Fm(x)h Fr(is)0 49988 y(in)382 b(the)f(language)i Fm(S)77 b Fr(".)562 b(Similarly)-108 b(,)394 b(w)-36 b(e)382 b(iden)-36 b(tify)383 b(eac)-36 b(h)382 b(in\014nite)f(binary)h(sequence)g(as)g(represen)-36 b(ting)382 b(the)0 51594 y(c)-36 b(haracteristic)434 b(sequence)f(of)i(a)f(subset)e(of)j Fh(N)p Fr(.)1951 53199 y(Let)449 b Fm(S)5 b(;)221 b(R)408 b Fl(2)396 b Fi(C)450 b Fr(and)f Fm(M)536 b Fl(2)396 b Fr(OTM.)626 b(W)-108 b(e)450 b(sa)-36 b(y)450 b Fm(S)557 b Fq(is)480 b(T)-100 b(uring)479 b(r)-66 b(e)g(ducible)478 b(to)i Fm(R)491 b Fq(via)479 b Fm(M)588 b Fr(and)450 b(w)-36 b(e)450 b(write)0 54804 y Fm(S)612 b Fl(\024)2445 55003 y Fv(T)3715 54804 y Fm(R)565 b Fq(via)554 b Fm(M)139 b Fr(,)556 b(if)531 b Fm(M)12485 54322 y Fj(R)13786 54804 y Fr(computes)f Fm(S)608 b Fr(\(that)530 b(is,)556 b(if)532 b Fm(M)28978 54322 y Fj(R)29748 54804 y Fr(\()p Fm(n)p Fr(\))i(=)h Fm(S)77 b Fr([0)221 b Fm(:)g(:)i(n)74 b Fl(\000)g Fr(1])532 b(for)f(all)h Fm(n)j Fl(2)g Fh(N)p Fr(\).)870 b(In)0 56409 y(this)493 b(case,)510 b(write)494 b Fm(R)482 b Fr(=)470 b Fm(M)139 b Fr(\()p Fm(S)77 b Fr(\).)759 b(W)-108 b(e)493 b(sa)-36 b(y)494 b Fm(S)598 b Fq(is)520 b(T)-100 b(uring)519 b(r)-66 b(e)g(ducible)519 b(to)h Fm(R)504 b Fr(and)493 b(w)-36 b(e)494 b(write)g Fm(S)548 b Fl(\024)47164 56608 y Fv(T)48370 56409 y Fm(R)11 b Fr(,)509 b(if)0 58014 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Fv(T)32085 61224 y Fr(\()p Fm(S)77 b Fr(\))368 b(=)h Fl(f)434 b Fm(R)380 b Fl(2)368 b Fi(C)656 b Fl(j)433 b Fm(R)380 b Fl(\021)44385 61423 y Fv(T)45489 61224 y Fm(S)644 b Fl(g)p Fr(.)1951 62829 y(Let)536 b Fm(S)5 b(;)221 b(R)556 b Fl(2)544 b Fi(C)537 b Fr(and)f Fm(M)684 b Fl(2)544 b Fr(OTM)536 b(suc)-36 b(h)536 b(that)g Fm(S)622 b Fl(\024)28459 63028 y Fv(T)29738 62829 y Fm(R)548 b Fr(via)537 b(the)g(oracle)g(T) -108 b(uring)536 b(mac)-36 b(hine)537 b Fm(M)139 b Fr(.)0 64434 y(Let)553 b(#\()p Fm(M)5437 63952 y Fj(R)6206 64434 y Fm(;)221 b(S)77 b Fr([0)221 b Fm(:)g(:)j(n)74 b Fl(\000)g Fr(1])q(\))553 b(denote)f(the)h Fq(query)575 b(usage)g(of)f Fm(M)31106 63952 y Fj(R)32451 64434 y Fq(on)g Fm(S)77 b Fr([0)221 b Fm(:)g(:)j(n)74 b Fl(\000)g Fr(1])q(,)583 b(the)553 b(index)g(of)h(the)0 66039 y(righ)-36 b(tmost)433 b(bit)h(of)g Fm(R)444 b Fr(queried)434 b(b)-36 b(y)433 b Fm(M)573 b Fr(when)433 b(computing)g Fm(S)77 b Fr([0)221 b Fm(:)g(:)j(n)74 b Fl(\000)g Fr(1])q(.)1951 67644 y(W)-108 b(e)408 b(sa)-36 b(y)410 b Fm(S)519 b Fq(is)441 b(we)-66 b(ak)442 b(truth-table)f Fr(\()p Fq(wtt)p Fr(\))g Fq(r)-66 b(e)g(ducible)441 b(to)g Fm(R)453 b Fq(via)441 b Fm(M)548 b Fr(and)408 b(w)-36 b(e)409 b(write)f Fm(S)447 b Fl(\024)43861 67843 y Fv(wtt)45697 67644 y Fm(R)452 b Fq(via)442 b Fm(M)139 b Fr(,)25175 72063 y(4)p eop end %%Page: 5 5 TeXDict begin 5 4 bop 0 1328 a Fr(if)466 b Fm(S)500 b Fl(\024)3557 1527 y Fv(T)4714 1328 y Fm(R)476 b Fr(via)467 b Fm(M)604 b Fr(and)464 b(there)h(is)g(a)h(computable)e(function)h Fm(q)470 b Fr(:)423 b Fh(N)g Fl(!)g Fh(N)465 b Fr(suc)-36 b(h)465 b(that,)472 b(for)466 b(all)g Fm(n)423 b Fl(2)f Fh(N)p Fr(,)0 2933 y(#\()p Fm(M)2987 2451 y Fj(R)3756 2933 y Fm(;)221 b(S)77 b Fr([0)221 b Fm(:)g(:)k(n)74 b Fl(\000)g Fr(1]\))369 b Fl(\024)g Fm(q)48 b Fr(\()p Fm(n)p Fr(\))433 b(\(see)h([7]\).)1951 4539 y(W)-108 b(e)472 b(sa)-36 b(y)473 b Fm(S)578 b Fq(is)501 b(b)-66 b(ounde)g(d)499 b(T)-100 b(uring)500 b Fr(\()p Fq(bT)p Fr(\))g Fq(r)-66 b(e)g(ducible)499 b(to)i Fm(R)511 b Fq(via)500 b Fm(M)612 b Fr(\(or)472 b(simply)h Fq(b)-66 b(ounde)g(d)500 b(r)-66 b(e)g(ducible)99 b Fr(\))0 6144 y(and)498 b(w)-36 b(e)500 b(write)f Fm(S)558 b Fl(\024)10355 6343 y Fv(bT)12093 6144 y Fm(R)536 b Fq(via)524 b Fm(M)139 b Fr(,)516 b(if)500 b Fm(S)557 b Fl(\024)21726 6343 y Fv(T)22941 6144 y Fm(R)510 b Fr(via)500 b Fm(M)638 b Fr(and)499 b(there)f(exists)i(a)f(constan)-36 b(t)499 b Fm(c)480 b Fl(2)g Fh(N)499 b Fr(suc)-36 b(h)0 7749 y(that,)462 b(for)456 b(ev)-36 b(ery)457 b Fm(n)408 b Fl(2)f Fh(N)p Fr(,)462 b(the)456 b(n)-36 b(um)g(b)36 b(er)454 b(of)j(bits)f(of)h Fm(R)467 b Fr(queried)456 b(when)f(computing)h Fm(S)77 b Fr([)p Fm(n)p Fr(])457 b(is)g(at)f(most)g Fm(c)0 9354 y Fr(\(see)434 b([9,)g(18)q(]\).)1951 10959 y(W)-108 b(e)331 b(sa)-36 b(y)331 b Fm(S)447 b Fq(is)370 b(truth-table)g Fr(\()p Fq(tt)p Fr(\))f Fq(r)-66 b(e)g(ducible)369 b(to)h Fm(R)381 b Fq(via)370 b Fm(M)470 b Fr(and)330 b(w)-36 b(e)331 b(write)g Fm(S)446 b Fl(\024)38859 11158 y Fv(tt)40015 10959 y Fm(R)381 b Fq(via)370 b Fm(M)139 b Fr(,)351 b(if)332 b Fm(S)446 b Fl(\024)48895 11158 y Fv(T)49999 10959 y Fm(R)0 12564 y Fr(via)431 b Fm(M)569 b Fr(and,)431 b(for)g(all)g Fm(R)11631 12082 y Fg(0)12310 12564 y Fl(2)369 b Fi(C)p Fr(,)431 b Fm(M)139 b Fr(\()p Fm(R)18340 12082 y Fg(0)18651 12564 y Fr(\))429 b(is)i(de\014ned;)f (that)g(is,)h Fm(M)569 b Fr(is)431 b(total)f(with)h(resp)36 b(ect)429 b(to)h(the)g(oracle)0 14169 y(\(see)k([19)q(]\).)1951 15774 y(Bounded)384 b(reductions)g(and)g(wtt)h(reductions)f(are)i (incomparable.)562 b(Ho)-36 b(w)g(ev)g(er,)396 b(ev)-36 b(ery)385 b(tt)g(reduction)0 17379 y(is)434 b(a)g(wtt)f(reduction.)1951 18984 y(Giv)-36 b(en)449 b(\001)394 b Fl(2)h(f)p Fr(tt)o Fm(;)221 b Fr(wtt)q Fm(;)g Fr(bT)q Fl(g)p Fr(,)453 b(de\014ne)447 b Fm(S)473 b Fl(\024)22502 19183 y Fv(\001)23736 18984 y Fm(R)11 b Fr(,)453 b Fm(S)472 b Fl(\021)27856 19183 y Fv(\001)29090 18984 y Fm(R)11 b Fr(,)453 b(span)33514 19298 y Fv(\001)34353 18984 y Fr(\()p Fm(S)77 b Fr(\))449 b(and)f(deg)41204 19298 y Fv(\001)42043 18984 y Fr(\()p Fm(S)77 b Fr(\))449 b(analogously)0 20589 y(to)434 b(their)f(coun)-36 b(terparts)432 b(for)i(T)-108 b(uring)433 b(reductions.)1951 22195 y(De\014ne)13363 25619 y Fm(\032)14034 25070 y Fg(\000)14034 25980 y Fj(M)15087 25619 y Fr(\()p Fm(S)5 b(;)221 b(R)11 b Fr(\))1108 b(=)e(lim)221 b(inf)22288 26416 y Fj(n)p Fg(!1)25669 24721 y Fr(#\()p Fm(M)28656 24239 y Fj(R)29425 24721 y Fm(;)g(S)77 b Fr([0)221 b Fm(:)g(:)k(n)74 b Fl(\000)g Fr(1])q(\))p 25669 25314 11090 54 v 30826 26531 a Fm(n)36891 25619 y(;)13363 28978 y(\032)14034 28428 y Fv(+)14034 29338 y Fj(M)15087 28978 y Fr(\()p Fm(S)5 b(;)221 b(R)11 b Fr(\))1108 b(=)e(lim)221 b(sup)22480 30033 y Fj(n)p Fg(!1)26053 28079 y Fr(#\()p Fm(M)29040 27597 y Fj(R)29810 28079 y Fm(;)g(S)77 b Fr([0)221 b Fm(:)g(:)j(n)74 b Fl(\000)g Fr(1])q(\))p 26053 28672 V 31210 29889 a Fm(n)37276 28978 y(:)0 32690 y Fr(Viewing)397 b Fm(R)407 b Fr(as)397 b(a)g(compressed)e(v)-36 b(ersion)397 b(of)g Fm(S)77 b Fr(,)404 b Fm(\032)23964 32140 y Fg(\000)23964 33050 y Fj(M)25017 32690 y Fr(\()p Fm(S)5 b(;)221 b(R)11 b Fr(\))397 b(and)f Fm(\032)31977 32140 y Fv(+)31977 33050 y Fj(M)33030 32690 y Fr(\()p Fm(S)5 b(;)221 b(R)11 b Fr(\))396 b(are)h(resp)36 b(ectiv)-36 b(ely)397 b(the)f(b)36 b(est-)0 34295 y(and)352 b(w)-36 b(orst-case)352 b(compression)g (ratios)h(as)g Fm(M)491 b Fr(decompresses)352 b Fm(R)363 b Fr(in)-36 b(to)352 b Fm(S)77 b Fr(.)552 b(Note)352 b(that)g(0)369 b Fl(\024)g Fm(\032)45144 33745 y Fg(\000)45144 34655 y Fj(M)46198 34295 y Fr(\()p Fm(S)5 b(;)221 b(R)11 b Fr(\))369 b Fl(\024)0 35900 y Fm(\032)671 35350 y Fv(+)671 36260 y Fj(M)1724 35900 y Fr(\()p Fm(S)5 b(;)221 b(R)11 b Fr(\))369 b Fl(\024)h(1)p Fr(.)0 38450 y(The)434 b(follo)-36 b(wing)435 b(lemma)f(is)g(useful)g(when)f(one)h(w)-36 b(an)g(ts)433 b(to)h(comp)36 b(ose)434 b(t)-36 b(w)g(o)433 b(reductions:)0 41162 y Fi(Lemma)512 b(1.1)f Fr(\(Dot)-36 b(y)445 b([4)q(]\))p Fi(.)559 b Fq(L)-66 b(et)474 b Fm(S)5 b(;)221 b(S)18848 40680 y Fg(0)19159 41162 y Fm(;)g(S)20618 40680 y Fg(00)21573 41162 y Fl(2)387 b Fi(C)475 b Fq(and)g Fm(M)28192 41361 y Fv(1)28719 41162 y Fm(;)221 b(M)30559 41361 y Fv(2)31473 41162 y Fl(2)387 b Fr(OTM)475 b Fq(such)h(that)f Fm(S)42874 40680 y Fg(0)43572 41162 y Fl(\024)44605 41361 y Fv(T)45728 41162 y Fm(S)552 b Fq(via)475 b Fm(M)50474 41361 y Fv(1)0 42767 y Fq(and)465 b Fm(S)3401 42285 y Fg(00)4336 42767 y Fl(\024)5369 42966 y Fv(T)6473 42767 y Fm(S)7350 42285 y Fg(0)8126 42767 y Fq(via)f Fm(M)11509 42966 y Fv(2)12035 42767 y Fq(.)597 b(Ther)-66 b(e)465 b(exists)f Fm(M)508 b Fl(2)368 b Fr(OTM)465 b Fq(such)h(that)f Fm(S)33439 42285 y Fg(00)34374 42767 y Fl(\024)35407 42966 y Fv(T)36511 42767 y Fm(S)542 b Fq(via)464 b Fm(M)604 b Fq(and:)14843 45701 y Fm(\032)15514 45151 y Fv(+)15514 46061 y Fj(M)16567 45701 y Fr(\()p Fm(S)17950 45152 y Fg(00)18516 45701 y Fm(;)221 b(S)77 b Fr(\))1108 b Fl(\024)f Fm(\032)24400 45151 y Fv(+)24400 46061 y Fj(M)25304 46184 y Fk(2)25820 45701 y Fr(\()p Fm(S)27203 45152 y Fg(00)27769 45701 y Fm(;)221 b(S)29228 45152 y Fg(0)29539 45701 y Fr(\))p Fm(\032)30716 45151 y Fv(+)30716 46061 y Fj(M)31620 46184 y Fk(1)32136 45701 y Fr(\()p Fm(S)33519 45152 y Fg(0)33830 45701 y Fm(;)g(S)77 b Fr(\))p Fm(:)14843 47638 y(\032)15514 47088 y Fg(\000)15514 47998 y Fj(M)16567 47638 y Fr(\()p Fm(S)17950 47089 y Fg(00)18516 47638 y Fm(;)221 b(S)77 b Fr(\))1108 b Fl(\024)f Fm(\032)24400 47088 y Fg(\000)24400 47998 y Fj(M)25304 48121 y Fk(2)25820 47638 y Fr(\()p Fm(S)27203 47089 y Fg(00)27769 47638 y Fm(;)221 b(S)29228 47089 y Fg(0)29539 47638 y Fr(\))p Fm(\032)30716 47088 y Fv(+)30716 47998 y Fj(M)31620 48121 y Fk(1)32136 47638 y Fr(\()p Fm(S)33519 47089 y Fg(0)33830 47638 y Fm(;)g(S)77 b Fr(\))p Fm(:)14843 49575 y(\032)15514 49025 y Fg(\000)15514 49935 y Fj(M)16567 49575 y Fr(\()p Fm(S)17950 49027 y Fg(00)18516 49575 y Fm(;)221 b(S)77 b Fr(\))1108 b Fl(\024)f Fm(\032)24400 49025 y Fv(+)24400 49935 y Fj(M)25304 50058 y Fk(2)25820 49575 y Fr(\()p Fm(S)27203 49027 y Fg(00)27769 49575 y Fm(;)221 b(S)29228 49027 y Fg(0)29539 49575 y Fr(\))p Fm(\032)30716 49025 y Fg(\000)30716 49935 y Fj(M)31620 50058 y Fk(1)32136 49575 y Fr(\()p Fm(S)33519 49027 y Fg(0)33830 49575 y Fm(;)g(S)77 b Fr(\))p Fm(:)0 52508 y Fr(\(The)576 b(last)h(b)36 b(ound)575 b(is)i(not)f(explicitly)i(stated)e(in)g([4)q(],)613 b(but)575 b(it)i(holds)f(for)h(the)f(same)g(reason)h(as)g(the)0 54114 y(second)433 b(one\).)0 56664 y(F)-108 b(or)397 b Fm(S)447 b Fl(2)368 b Fi(C)p Fr(,)406 b(the)397 b Fq(lower)432 b(and)g(upp)-66 b(er)432 b(T)-100 b(uring)432 b(c)-66 b(ompr)g(ession)430 b(r)-66 b(atios)432 b(of)g Fm(S)475 b Fr(are)398 b(resp)36 b(ectiv)-36 b(ely)398 b(de\014ned)f(as)11410 59597 y Fm(\032)12081 59048 y Fg(\000)12868 59597 y Fr(\()p Fm(S)77 b Fr(\))1106 b(=)1972 b(min)18869 60426 y Fj(R)5 b Fg(2)p Fe(C)17982 61207 y Fj(M)94 b Fg(2)p Fv(OTM)22102 58521 y Fd(\010)23009 59597 y Fm(\032)23680 59047 y Fg(\000)23680 59957 y Fj(M)24733 59597 y Fr(\()p Fm(S)5 b(;)221 b(R)11 b Fr(\))28567 58468 y Fd(\014)28567 59265 y(\014)29665 59597 y Fm(S)446 b Fl(\024)31944 59796 y Fv(T)33048 59597 y Fm(R)f Fr(via)434 b Fm(M)38011 58521 y Fd(\011)39008 59597 y Fm(;)11410 62967 y(\032)12081 62419 y Fv(+)12868 62967 y Fr(\()p Fm(S)77 b Fr(\))1106 b(=)1972 b(min)18869 63796 y Fj(R)5 b Fg(2)p Fe(C)17982 64577 y Fj(M)94 b Fg(2)p Fv(OTM)22102 61891 y Fd(\010)23009 62967 y Fm(\032)23680 62417 y Fv(+)23680 63327 y Fj(M)24733 62967 y Fr(\()p Fm(S)5 b(;)221 b(R)11 b Fr(\))28567 61838 y Fd(\014)28567 62635 y(\014)29665 62967 y Fm(S)446 b Fl(\024)31944 63166 y Fv(T)33048 62967 y Fm(R)f Fr(via)434 b Fm(M)38011 61891 y Fd(\011)39008 62967 y Fm(:)0 67222 y Fr(Dot)-36 b(y)434 b([4)q(])g(sho)-36 b(w)g(ed)433 b(that)g(the)g(ab)36 b(o)-36 b(v)g(e)434 b(minima)g(exist.)579 b(Note)434 b(that)f(0)370 b Fl(\024)f Fm(\032)35605 66740 y Fg(\000)36392 67222 y Fr(\()p Fm(S)77 b Fr(\))369 b Fl(\024)g Fm(\032)40723 66740 y Fv(+)41510 67222 y Fr(\()p Fm(S)77 b Fr(\))369 b Fl(\024)g Fr(1.)25175 72063 y(5)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 0 1328 a Fi(Constructiv)-42 b(e)423 b(Dimension.)1303 b Fr(Lutz)365 b([12)q(])i(giv)-36 b(es)368 b(an)e(in)-36 b(tro)36 b(duction)365 b(to)i(the)f(theory)g(of)h (constructiv)-36 b(e)0 2933 y(dimension.)862 b(W)-108 b(e)528 b(use)g(Ma)-36 b(y)g(ordomo's)529 b(c)-36 b(haracterization)529 b([14])g(of)g(the)e(constructiv)-36 b(e)528 b(dimensions)g(of)0 4539 y(sequences.)1117 b(F)-108 b(or)613 b(all)g Fm(S)752 b Fl(2)674 b Fi(C)p Fr(,)659 b(the)612 b Fq(c)-66 b(onstructive)628 b(Hausdor\013)j(dimension)711 b Fr(and)612 b(the)h Fq(c)-66 b(onstructive)0 6144 y(p)g(acking)463 b(dimension)532 b Fr(of)434 b Fm(S)511 b Fr(are)433 b(resp)36 b(ectiv)-36 b(ely)435 b(de\014ned)d(as)4828 9490 y(dim)6995 9689 y Fv(H)7756 9490 y Fr(\()p Fm(S)77 b Fr(\))368 b(=)h(lim)221 b(inf)11969 10287 y Fj(n)p Fg(!1)15350 8591 y Fr(C\()p Fm(S)77 b Fr([0)221 b Fm(:)g(:)j(n)74 b Fl(\000)g Fr(1])q(\))p 15350 9184 8196 54 v 19060 10401 a Fm(n)24112 9490 y Fr(and)433 b(dim)28809 9689 y Fv(P)29504 9490 y Fr(\()p Fm(S)77 b Fr(\))369 b(=)f(lim)221 b(sup)33909 10545 y Fj(n)p Fg(!1)37483 8591 y Fr(C\()p Fm(S)77 b Fr([0)221 b Fm(:)g(:)j(n)74 b Fl(\000)g Fr(1]\))p 37483 9184 V 41192 10401 a Fm(n)45811 9490 y(;)0 12867 y Fr(where)519 b(C\()p Fm(w)36 b Fr(\))519 b(denotes)g(the)g Fq(Kolmo)-66 b(gor)g(ov)542 b(c)-66 b(omplexity)634 b Fr(of)520 b Fm(w)551 b Fl(2)514 b(f)p Fr(0)p Fm(;)221 b Fr(1)p Fl(g)35804 12385 y Fg(\003)36851 12867 y Fr(\(see)519 b([10)q(]\).)836 b(If)520 b(dim)46824 13066 y Fv(H)47585 12867 y Fr(\()p Fm(S)77 b Fr(\))514 b(=)0 14472 y(dim)2168 14671 y Fv(P)2863 14472 y Fr(\()p Fm(S)77 b Fr(\),)525 b(w)-36 b(e)506 b(sa)-36 b(y)507 b Fm(S)584 b Fr(is)506 b(a)h Fq(r)-66 b(e)g(gular)648 b Fr(sequence.)796 b(Dot)-36 b(y)507 b([4)q(])g(sho)-36 b(w)g(ed)506 b(that,)524 b(for)507 b(all)g Fm(S)570 b Fl(2)492 b Fi(C)p Fr(,)525 b Fm(\032)46820 13990 y Fg(\000)47607 14472 y Fr(\()p Fm(S)77 b Fr(\))492 b(=)0 16077 y(dim)2168 16276 y Fv(H)2928 16077 y Fr(\()p Fm(S)77 b Fr(\))433 b(and)g Fm(\032)8450 15595 y Fv(+)9237 16077 y Fr(\()p Fm(S)77 b Fr(\))369 b(=)g(dim)15044 16276 y Fv(P)15739 16077 y Fr(\()p Fm(S)77 b Fr(\).)1951 17682 y(F)-108 b(or)592 b(all)i Fm(X)745 b Fl(\022)640 b Fi(C)p Fr(,)633 b(the)593 b Fq(c)-66 b(onstructive)609 b(Hausdor\013)j (dimension)691 b Fr(and)592 b(the)g Fq(c)-66 b(onstructive)610 b(p)-66 b(acking)0 19287 y(dimension)531 b Fr(of)435 b Fm(X)538 b Fr(are)434 b(resp)36 b(ectiv)-36 b(ely)434 b(de\014ned)e(as)9900 21975 y(dim)12067 22174 y Fv(H)12828 21975 y Fr(\()p Fm(X)104 b Fr(\))369 b(=)436 b(sup)16773 23059 y Fj(S)50 b Fg(2)p Fj(X)19086 21975 y Fr(dim)21254 22174 y Fv(H)22014 21975 y Fr(\()p Fm(S)77 b Fr(\))433 b(and)h(dim)29033 22174 y Fv(P)29729 21975 y Fr(\()p Fm(X)104 b Fr(\))369 b(=)436 b(sup)33674 23059 y Fj(S)50 b Fg(2)p Fj(X)35987 21975 y Fr(dim)38155 22174 y Fv(P)38850 21975 y Fr(\()p Fm(S)77 b Fr(\))p Fm(:)0 26653 y Fs(2)2152 b(Constructiv)-60 b(e)716 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Fm(N)28131 16897 y Fj(S)28807 17379 y Fr(\()p Fm(n)p Fr(\))339 b(sim)-36 b(ulates)338 b Fm(M)37922 16897 y Fj(S)38599 17379 y Fr(\()p Fm(n)p Fr(\).)547 b(In)338 b(parallel,)359 b(for)339 b(all)0 18984 y(in)-36 b(tegers)461 b Fm(m)415 b(>)h(n)p Fr(,)468 b Fm(N)600 b Fr(searc)-36 b(hes)461 b(for)g(a)h(program)f(of)g(length)g(at)g(most) g Fm(\013)35664 18502 y Fg(0)35976 18984 y Fm(m)f Fr(computing)h Fm(S)77 b Fr([0)221 b Fm(:)g(:)j(m)74 b Fl(\000)g Fr(1].)0 20589 y(If)456 b Fm(N)594 b Fr(\014nds)455 b(suc)-36 b(h)455 b(a)h(program)g(b)36 b(efore)456 b(the)f(sim)-36 b(ulation)456 b(of)h Fm(M)30821 20107 y Fj(S)31498 20589 y Fr(\()p Fm(n)p Fr(\))f(terminates,)461 b(then)455 b Fm(N)594 b Fr(outputs)454 b(0.)0 22195 y(If)550 b(instead)f(the)g(sim) -36 b(ulation)549 b(of)h Fm(M)17814 21712 y Fj(S)18491 22195 y Fr(\()p Fm(n)p Fr(\))g(halts)f(b)36 b(efore)550 b(suc)-36 b(h)548 b(a)i(short)e(program)i(is)f(found,)578 b(then)549 b Fm(N)0 23800 y Fr(outputs)432 b Fm(R)11 b Fr([)p Fm(n)p Fr(],)435 b(the)e(output)f(bit)i(of)g Fm(M)19476 23318 y Fj(S)20153 23800 y Fr(\()p Fm(n)p Fr(\).)1951 25405 y(If)520 b(dim)5505 25604 y Fv(H)6265 25405 y Fr(\()p Fm(S)77 b Fr(\))514 b Fm(<)h(\013)11030 24923 y Fg(0)11341 25405 y Fr(,)541 b(then)518 b(for)i(in\014nitely)f (man)-36 b(y)519 b Fm(m)c Fl(2)f Fh(N)p Fr(,)541 b(C\()p Fm(S)77 b Fr([0)221 b Fm(:)g(:)j(m)74 b Fl(\000)g Fr(1]\))514 b Fl(\024)h Fm(\013)42899 24923 y Fg(0)43211 25405 y Fm(m)p Fr(.)834 b(Therefore)0 27010 y Fm(N)1181 26528 y Fj(S)2233 27010 y Fr(halts,)387 b(although)375 b(the)g(output)f (sequence)h Fm(N)139 b Fr(\()p Fm(S)77 b Fr(\))374 b(ma)-36 b(y)376 b(con)-36 b(tain)375 b(a)h(lot)f(of)h(0's,)388 b(whic)-36 b(h)375 b(is)h(acceptable)0 28615 y(b)36 b(ecause)433 b(w)-36 b(e)434 b(do)g(not)f(care)h(what)g Fm(N)571 b Fr(outputs)433 b(if)h(dim)26594 28814 y Fv(H)27354 28615 y Fr(\()p Fm(S)77 b Fr(\))369 b Fm(<)f(\013)31827 28133 y Fg(0)32139 28615 y Fr(.)1951 30220 y(If)583 b(dim)5568 30419 y Fv(H)6328 30220 y Fr(\()p Fm(S)77 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