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Unknown | 1991-07-09 | 5.8 KB |
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MacOS 8.1
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Win98
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DOS
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Confidence | Program | Detection | Match Type | Support
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100%
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| data
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hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 4f 00 01 00 03 98 81 0e | 54 68 69 73 20 70 72 6f |O.......|This pro|
|00000010| 67 72 61 6d 20 69 6d 70 | 6c 69 6d 65 6e 74 73 20 |gram imp|liments |
|00000020| 74 68 65 20 72 65 64 75 | 63 74 69 6f 6e 20 61 6c |the redu|ction al|
|00000030| 67 6f 72 69 74 68 6d 20 | 6f 66 20 4c 65 6e 67 73 |gorithm |of Lengs|
|00000040| 74 72 61 2c 20 4c 65 6e | 67 73 74 72 61 2c 0d 9e |tra, Len|gstra,..|
|00000050| 00 02 00 03 98 00 00 61 | 6e 64 20 4c 6f 76 61 73 |.......a|nd Lovas|
|00000060| 7a 20 28 4d 61 74 68 2e | 20 41 6e 6e 2e 20 32 36 |z (Math.| Ann. 26|
|00000070| 31 20 28 31 39 38 32 29 | 20 35 31 35 2d 35 33 34 |1 (1982)| 515-534|
|00000080| 29 20 74 6f 20 6f 62 74 | 61 69 6e 20 61 20 22 72 |) to obt|ain a "r|
|00000090| 65 64 75 63 65 64 20 62 | 61 73 69 73 22 0d e7 00 |educed b|asis"...|
|000000a0| 03 00 03 98 00 00 66 6f | 72 20 61 20 70 6f 73 69 |......fo|r a posi|
|000000b0| 74 69 76 65 20 64 65 66 | 69 6e 69 74 65 20 72 65 |tive def|inite re|
|000000c0| 61 6c 20 76 61 6c 75 65 | 64 20 62 69 6c 69 6e 65 |al value|d biline|
|000000d0| 61 72 20 66 6f 72 6d 20 | 41 28 2d 2c 2d 29 20 6f |ar form |A(-,-) o|
|000000e0| 6e 20 5a 5e 6e 2e 0d 33 | 01 04 00 03 98 00 00 49 |n Z^n..3|.......I|
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|00000130| 6d 2e 0d 3c 01 05 00 03 | 98 00 00 0d 85 01 06 00 |m..<....|........|
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|00000270| 84 02 5a 00 81 02 4e 00 | 29 98 41 0f 20 20 20 20 |..Z...N.|).A. |
|00000280| 20 20 20 20 75 73 65 64 | 20 62 79 20 2a 53 45 41 | used| by *SEA|
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|000002b0| 00 03 98 00 00 20 53 65 | 74 20 75 70 20 61 20 66 |..... Se|t up a f|
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|000003f0| 0d 20 04 54 00 03 88 f5 | 09 50 52 49 4e 54 46 4f |. .T....|.PRINTFO|
|00000400| 52 4d f0 f3 88 f5 09 50 | 52 49 4e 54 42 41 53 45 |RM.....P|RINTBASE|
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|00000430| 87 f1 55 00 0d 3e 04 64 | 00 03 98 00 00 0d 86 04 |..U..>.d|........|
|00000440| 6e 00 03 98 00 00 20 53 | 75 62 72 6f 75 74 69 6e |n..... S|ubroutin|
|00000450| 65 20 74 6f 20 63 6f 6d | 70 75 74 65 20 74 68 65 |e to com|pute the|
|00000460| 20 41 2d 69 6e 6e 65 72 | 20 70 72 6f 64 75 63 74 | A-inner| product|
|00000470| 20 6f 66 20 64 28 6e 2c | 2d 29 20 61 6e 64 20 64 | of d(n,|-) and d|
|00000480| 28 6d 2c 2d 29 0d c9 04 | 78 00 03 98 00 00 20 41 |(m,-)...|x..... A|
|00000490| 28 29 20 6d 75 73 74 20 | 62 65 20 69 6e 69 74 69 |() must |be initi|
|000004a0| 61 6c 69 7a 65 64 20 74 | 6f 20 74 68 65 20 64 65 |alized t|o the de|
|000004b0| 66 69 6e 69 74 65 20 66 | 6f 72 6d 20 69 6e 20 71 |finite f|orm in q|
|000004c0| 75 65 73 74 69 6f 6e 2e | 0d d2 04 82 00 03 98 00 |uestion.|........|
|000004d0| 00 0d ef 04 8c 00 03 f5 | 02 49 50 00 00 28 26 84 |........|.IP..(&.|
|000004e0| 02 44 00 c2 83 02 4e 00 | c2 83 02 4d 00 29 0d ff |.D....N.|...M.)..|
|000004f0| 04 8d 00 03 ba 83 02 49 | 00 c2 83 02 4a 00 0d 0a |.......I|....J...|
|00000500| 05 8e 00 03 a8 83 02 49 | 50 0d 64 05 96 00 03 89 |.......I|P.d.....|
|00000510| 83 02 49 00 d1 f0 8a 81 | 02 4e 00 c0 89 83 02 4a |..I.....|.N.....J|
|00000520| 00 d1 f0 8a 81 02 4e 00 | c0 83 02 49 50 d1 83 02 |......N.|...IP...|
|00000530| 49 50 dd 84 02 41 00 83 | 02 49 00 c2 83 02 4a 00 |IP...A..|.I....J.|
|00000540| 29 e5 84 02 44 00 83 02 | 4e 00 c2 83 02 49 00 29 |)...D...|N....I.)|
|00000550| e5 84 02 44 00 83 02 4d | 00 c2 83 02 4a 00 29 c0 |...D...M|....J.).|
|00000560| 8c c0 8c 0d 6b 05 a0 00 | 03 95 0d 74 05 c8 00 03 |....k...|...t....|
|00000570| 98 00 00 0d 82 05 d2 00 | 03 f5 04 4d 41 49 4e 00 |........|...MAIN.|
|00000580| 00 0d 8b 05 dc 00 03 98 | 49 13 0d d7 05 e6 00 03 |........|I.......|
|00000590| 98 00 00 20 41 74 20 61 | 6e 79 20 74 69 6d 65 20 |... At a|ny time |
|000005a0| 64 75 72 69 6e 67 20 74 | 68 65 20 72 65 64 75 63 |during t|he reduc|
|000005b0| 74 69 6f 6e 2c 20 42 28 | 69 2c 2d 29 20 69 73 20 |tion, B(|i,-) is |
|000005c0| 74 68 65 20 69 74 68 20 | 62 61 73 69 73 20 65 6c |the ith |basis el|
|000005d0| 65 6d 65 6e 74 2e 0d 1f | 06 f0 00 03 98 00 00 20 |ement...|....... |
|000005e0| 53 6f 20 42 41 42 74 20 | 69 73 20 74 68 65 20 6d |So BABt |is the m|
|000005f0| 61 74 72 69 78 20 6f 66 | 20 74 68 65 20 66 6f 72 |atrix of| the for|
|00000600| 6d 20 77 69 74 68 20 72 | 65 73 70 65 63 74 20 74 |m with r|espect t|
|00000610| 6f 20 74 68 65 20 42 2d | 62 61 73 69 73 2e 0d 44 |o the B-|basis..D|
|00000620| 06 fa 00 03 98 00 00 20 | 20 28 42 74 20 6d 65 61 |....... | (Bt mea|
|00000630| 6e 73 20 74 72 61 6e 73 | 70 6f 73 65 20 6f 66 20 |ns trans|pose of |
|00000640| 42 2e 29 0d 8d 06 04 01 | 03 98 00 00 20 57 65 20 |B.).....|.... We |
|00000650| 73 74 61 72 74 20 77 69 | 74 68 20 74 68 65 20 73 |start wi|th the s|
|00000660| 74 61 6e 64 61 72 64 20 | 62 61 73 69 73 2c 20 74 |tandard |basis, t|
|00000670| 68 6f 75 67 68 20 74 68 | 69 73 20 69 73 20 6e 6f |hough th|is is no|
|00000680| 74 20 65 73 73 65 6e 74 | 69 61 6c 2e 0d 96 06 0e |t essent|ial.....|
|00000690| 01 03 98 00 00 0d d6 06 | 18 01 03 a8 a2 84 02 42 |........|.......B|
|000006a0| 00 f0 c3 81 02 4e 00 c2 | f0 c3 81 02 4e 00 29 c0 |.....N..|....N.).|
|000006b0| 89 83 02 49 00 d1 f0 8a | 81 02 4e 00 c0 84 02 42 |...I....|..N....B|
|000006c0| 00 83 02 49 00 c2 83 02 | 49 00 29 d1 f1 01 00 c0 |...I....|I.).....|
|000006d0| 8c 83 02 49 00 0d df 06 | 22 01 03 98 ab 14 0d 25 |...I....|"......%|
|000006e0| 07 2c 01 03 98 00 00 20 | 4d 20 77 69 6c 6c 20 62 |.,..... |M will b|
|000006f0| 65 20 61 20 6c 6f 77 65 | 72 20 74 72 69 61 6e 67 |e a lowe|r triang|
|00000700| 75 6c 61 72 20 6d 61 74 | 72 69 78 20 77 69 74 68 |ular mat|rix with|
|00000710| 20 31 27 73 20 6f 6e 20 | 74 68 65 20 64 69 61 67 | 1's on |the diag|
|00000720| 6f 6e 61 6c 0d 69 07 36 | 01 03 98 00 00 20 28 69 |onal.i.6|..... (i|
|00000730| 74 73 20 65 6e 74 72 69 | 65 73 20 62 65 6c 6f 77 |ts entri|es below|
|00000740| 20 74 68 65 20 64 69 61 | 67 6f 6e 61 6c 20 61 72 | the dia|gonal ar|
|00000750| 65 20 4d 28 69 2c 6a 29 | 29 2e 20 20 57 65 20 64 |e M(i,j)|). We d|
|00000760| 6f 20 61 20 47 72 61 6d | 0d b5 07 40 01 03 98 00 |o a Gram|...@....|
|00000770| 00 20 72 65 64 75 63 74 | 69 6f 6e 20 74 6f 20 66 |. reduct|ion to f|
|00000780| 69 6e 64 20 43 20 61 6e | 64 20 4d 20 73 75 63 68 |ind C an|d M such|
|00000790| 20 74 68 61 74 20 42 3d | 4d 43 20 61 6e 64 20 43 | that B=|MC and C|
|000007a0| 41 43 74 3d 44 69 61 67 | 28 56 31 2c 2e 2e 2e 2c |ACt=Diag|(V1,...,|
|000007b0| 56 6e 29 2e 0d f5 07 4a | 01 03 98 00 00 20 49 6e |Vn)....J|..... In|
|000007c0| 20 70 61 72 74 69 63 75 | 6c 61 72 2c 20 28 41 20 | particu|lar, (A |
|000007d0| 3d 29 20 42 41 42 74 20 | 3d 20 4d 56 4d 74 2c 20 |=) BABt |= MVMt, |
|000007e0| 77 68 65 72 65 20 56 20 | 69 73 20 64 69 61 67 6f |where V |is diago|
|000007f0| 6e 61 6c 2e 0d fe 07 54 | 01 03 98 00 00 0d 21 08 |nal....T|......!.|
|00000800| 5e 01 03 99 22 49 6e 69 | 74 69 61 6c 69 7a 69 6e |^..."Ini|tializin|
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|00000820| 0d 4e 08 68 01 03 a2 84 | 02 43 00 f0 c3 81 02 4e |.N.h....|.C.....N|
|00000830| 00 c2 f0 c3 81 02 4e 00 | 29 d1 a2 84 02 42 00 f0 |......N.|)....B..|
|00000840| c3 81 02 4e 00 c2 f0 c3 | 81 02 4e 00 29 0d 60 08 |...N....|..N.).`.|
|00000850| 72 01 03 89 83 02 49 00 | d1 f0 8a 81 02 4e 00 0d |r.....I.|.....N..|
|00000860| 76 08 7c 01 03 89 83 02 | 4a 00 d1 f0 8a 83 02 49 |v.|.....|J......I|
|00000870| 00 de f1 01 00 0d b2 08 | 86 01 03 88 f5 02 49 50 |........|......IP|
|00000880| cb f2 28 26 84 02 43 00 | c2 83 02 49 00 c2 83 02 |..(&..C.|...I....|
|00000890| 4a 00 29 c0 84 02 4d 00 | 83 02 49 00 c2 83 02 4a |J.)...M.|..I....J|
|000008a0| 00 29 d1 83 02 49 50 e6 | 84 02 56 00 83 02 4a 00 |.)...IP.|..V...J.|
|000008b0| 29 0d 06 09 90 01 03 89 | 83 02 4b 00 d1 f0 8a 81 |).......|..K.....|
|000008c0| 02 4e 00 c0 84 02 43 00 | 83 02 49 00 c2 83 02 4b |.N....C.|..I....K|
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|000008f0| e5 84 02 43 00 83 02 4a | 00 c2 83 02 4b 00 29 c0 |...C...J|....K.).|
|00000900| 8c 83 02 4b 00 0d 11 09 | 9a 01 03 8c 83 02 4a 00 |...K....|......J.|
|00000910| 0d 3e 09 a4 01 03 88 f5 | 02 49 50 cb f2 28 26 84 |.>......|.IP..(&.|
|00000920| 02 43 00 c2 83 02 49 00 | c2 83 02 49 00 29 c0 84 |.C....I.|...I.)..|
|00000930| 02 56 00 83 02 49 00 29 | d1 83 02 49 50 0d 49 09 |.V...I.)|...IP.I.|
|00000940| ae 01 03 8c 83 02 49 00 | 0d 52 09 b8 01 03 98 fa |......I.|.R......|
|00000950| 16 0d 96 09 c2 01 03 98 | 00 00 20 57 65 20 72 65 |........|.. We re|
|00000960| 2d 75 73 65 20 43 28 2d | 2c 2d 29 20 74 6f 20 68 |-use C(-|,-) to h|
|00000970| 6f 6c 64 20 42 5e 2d 31 | 20 28 61 63 74 75 61 6c |old B^-1| (actual|
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|00000990| 42 29 5e 2d 31 0d da 09 | cc 01 03 98 00 00 20 66 |B)^-1...|...... f|
|000009a0| 6f 72 20 61 6e 79 20 69 | 6e 69 74 69 61 6c 20 63 |or any i|nitial c|
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|000009c0| 2d 31 20 69 73 20 6e 6f | 74 20 6e 65 65 64 65 64 |-1 is no|t needed|
|000009d0| 20 66 6f 72 20 6d 6f 73 | 74 0d 23 0a d6 01 03 98 | for mos|t.#.....|
|000009e0| 00 00 20 61 70 70 6c 69 | 63 61 74 69 6f 6e 73 2c |.. appli|cations,|
|000009f0| 20 73 6f 20 74 68 65 20 | 63 6f 64 65 20 74 6f 20 | so the |code to |
|00000a00| 63 6f 6d 70 75 74 65 20 | 69 74 20 63 61 6e 20 75 |compute |it can u|
|00000a10| 73 75 61 6c 6c 79 20 62 | 65 20 64 65 6c 65 74 65 |sually b|e delete|
|00000a20| 64 2e 0d 44 0a e0 01 03 | 98 00 00 20 57 65 20 66 |d..D....|... We f|
|00000a30| 69 72 73 74 20 69 6e 69 | 74 69 61 6c 69 7a 65 20 |irst ini|tialize |
|00000a40| 69 74 2e 0d 4d 0a ea 01 | 03 98 00 00 0d 8d 0a f4 |it..M...|........|
|00000a50| 01 03 a8 a2 84 02 43 00 | f0 c3 81 02 4e 00 c2 f0 |......C.|....N...|
|00000a60| c3 81 02 4e 00 29 c0 89 | 83 02 49 00 d1 f0 8a 81 |...N.)..|..I.....|
|00000a70| 02 4e 00 c0 84 02 43 00 | 83 02 49 00 c2 83 02 49 |.N....C.|..I....I|
|00000a80| 00 29 d1 f1 01 00 c0 8c | 83 02 49 00 0d 96 0a fe |.)......|..I.....|
|00000a90| 01 03 98 63 18 0d df 0a | 08 02 03 98 00 00 20 54 |...c....|...... T|
|00000aa0| 68 65 20 6d 61 69 6e 20 | 72 65 64 75 63 74 69 6f |he main |reductio|
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|00000ac0| 6f 77 73 2e 20 20 49 74 | 20 6f 70 65 72 61 74 65 |ows. It| operate|
|00000ad0| 73 20 6f 6e 20 74 68 65 | 20 62 61 73 69 73 0d 25 |s on the| basis.%|
|00000ae0| 0b 12 02 03 98 00 00 20 | 42 20 73 6f 20 74 68 61 |....... |B so tha|
|00000af0| 74 20 61 66 74 65 72 20 | 72 65 64 75 63 74 69 6f |t after |reductio|
|00000b00| 6e 20 77 65 20 68 61 76 | 65 20 6e 65 77 20 42 2c |n we hav|e new B,|
|00000b10| 4d 2c 56 20 73 74 69 6c | 6c 20 73 61 74 69 73 66 |M,V stil|l satisf|
|00000b20| 79 69 6e 67 0d 69 0b 1c | 02 03 98 00 00 20 42 41 |ying.i..|..... BA|
|00000b30| 42 74 3d 4d 56 4d 74 2c | 20 62 75 74 20 77 69 74 |Bt=MVMt,| but wit|
|00000b40| 68 20 61 6c 6c 20 4d 69 | 6a 20 3c 3d 20 2e 35 20 |h all Mi|j <= .5 |
|00000b50| 61 6e 64 20 77 69 74 68 | 20 61 20 63 6f 6e 73 74 |and with| a const|
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|00000b70| 00 20 74 68 65 20 65 6e | 74 72 69 65 73 20 6f 66 |. the en|tries of|
|00000b80| 20 56 20 28 77 68 69 63 | 68 20 69 6d 70 6c 69 65 | V (whic|h implie|
|00000b90| 73 20 56 28 6b 29 20 3e | 3d 20 56 28 6b 2d 31 29 |s V(k) >|= V(k-1)|
|00000ba0| 2a 28 50 50 2d 2e 32 35 | 29 20 29 2e 0d b6 0b 30 |*(PP-.25|) )....0|
|00000bb0| 02 03 98 00 00 0d d1 0b | 3a 02 03 99 22 53 54 41 |........|:..."STA|
|00000bc0| 52 54 49 4e 47 20 52 45 | 44 55 43 54 49 4f 4e 22 |RTING RE|DUCTION"|
|00000bd0| 0d e7 0b 44 02 03 83 02 | 4b 00 d1 f1 01 00 c0 87 |...D....|K.......|
|00000be0| f5 02 52 31 a3 1a 0d 5c | 0c 4e 02 03 f5 02 52 32 |..R1...\|.N....R2|
|00000bf0| 00 00 83 02 4d 00 d1 84 | 02 4d 00 83 02 4b 00 c2 |....M...|.M...K..|
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|00000c20| 4d 00 e5 84 02 56 00 83 | 02 4b 00 de f1 01 00 29 |M....V..|.K.....)|
|00000c30| c0 84 02 4d 00 83 02 4b | 00 c2 83 02 4b 00 de f1 |...M...K|....K...|
|00000c40| 01 00 29 d1 83 02 4d 00 | e5 84 02 56 00 83 02 4b |..)...M.|...V...K|
|00000c50| 00 de f1 01 00 29 e6 83 | 02 56 00 0d 9b 0c 58 02 |.....)..|.V....X.|
|00000c60| 03 84 02 56 00 83 02 4b | 00 29 d1 84 02 56 00 83 |...V...K|.)...V..|
|00000c70| 02 4b 00 de f1 01 00 29 | e5 84 02 56 00 83 02 4b |.K.....)|...V...K|
|00000c80| 00 29 e6 83 02 56 00 c0 | 84 02 56 00 83 02 4b 00 |.)...V..|..V...K.|
|00000c90| de f1 01 00 29 d1 83 02 | 56 00 0d c9 0c 62 02 03 |....)...|V....b..|
|00000ca0| a5 a2 84 02 42 00 83 02 | 4b 00 c2 f0 c3 81 02 4e |....B...|K......N|
|00000cb0| 00 29 c2 a2 84 02 42 00 | 83 02 4b 00 de f1 01 00 |.)....B.|..K.....|
|00000cc0| c2 f0 c3 81 02 4e 00 29 | 0d f7 0c 63 02 03 a5 a2 |.....N.)|...c....|
|00000cd0| 84 02 43 00 f0 c3 81 02 | 4e 00 c2 83 02 4b 00 29 |..C.....|N....K.)|
|00000ce0| c2 a2 84 02 43 00 f0 c3 | 81 02 4e 00 c2 83 02 4b |....C...|..N....K|
|00000cf0| 00 de f1 01 00 29 0d 39 | 0d 6c 02 03 8d e6 19 83 |.....).9|.l......|
|00000d00| 02 4b 00 d2 f1 01 00 8e | a5 a2 84 02 4d 00 83 02 |.K......|....M...|
|00000d10| 4b 00 c2 f0 c3 83 02 4b | 00 de f1 02 00 29 c2 a2 |K......K|.....)..|
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|00000d30| 02 4b 00 de f1 02 00 29 | 0d 52 0d 76 02 03 89 83 |.K.....)|.R.v....|
|00000d40| 02 49 00 d1 83 02 4b 00 | dd f1 01 00 8a 81 02 4e |.I....K.|.......N|
|00000d50| 00 0d d3 0d 80 02 03 83 | 02 56 00 d1 84 02 4d 00 |........|.V....M.|
|00000d60| 83 02 49 00 c2 83 02 4b | 00 29 c0 84 02 4d 00 83 |..I....K|.)...M..|
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