abaababaabaababa 7 f 0 b f 1 a

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フィボナッチ文字列abaababaabaababaの さまざまな表現 7 f 0 = b f 1 = a fn = fn-1・

フィボナッチ文字列abaababaabaababaの さまざまな表現 7 f 0 = b f 1 = a fn = fn-1・ fn-2 (n≥ 2) 4 漸化式,文法 2 1 a b f 2=ab f 3=aba f 4=abaab f 5=abaababa f 6=abaabaab f 7=abaababaababa 6 5 3 OBDD風 方程式 compress gzip bzip 2 : 圧縮

abaababaabaababaabaababaabaababaabaababaabaababaabaababaab abaabaababaabaababaabaab abaababaabaababaabaababa ababaabaababaabaababaaba baabaababaabaababaabaaba baababaabaababaabaababaa babaabaababaabaababaabaa BW変換すると b 9 a 15 になる bzip 2で

abaababaabaababaabaababaabaababaabaababaabaababaabaababaab abaabaababaabaababaabaab abaababaabaababaabaababa ababaabaababaabaababaaba baabaababaabaababaabaaba baababaabaababaabaababaa babaabaababaabaababaabaa BW変換すると b 9 a 15 になる bzip 2で 圧縮しやすい

フィボナッチ文字列はbzip 2でよく縮む f 2=ab BW変換 f 3=aba f 4=abaab BW逆変換 f 5=abaababa f 6=abaabaab

フィボナッチ文字列はbzip 2でよく縮む f 2=ab BW変換 f 3=aba f 4=abaab BW逆変換 f 5=abaababa f 6=abaabaab f 7=abaababaababa b 1 a 1  b 1 a 2  b 2 a 3  b 3 a 5 b 5 a 8  b 8 a 13  

OBDD ⋍ MPMG SLP MPMG T = abaababa x 3 x2 X 8 x2

OBDD ⋍ MPMG SLP MPMG T = abaababa x 3 x2 X 8 x2 X 6 x 1 x 1 a OBDD b X 3 X 7 X 4 X 5 X 1 X 2 X 1 a b a b a X 1 = a X 2 = b X 3 = X 1 X 2 X 4 = X 1 X 5 = X 2 X 1 X 6 = X 3 X 4 X 7 = X 5 X 8 = X 6 X 7

Good Compression for Repetitive Text T = (aaab)n X 7 X 6 X 5

Good Compression for Repetitive Text T = (aaab)n X 7 X 6 X 5 X 3 X 5 X 4 X 3 X 4 X 1 X 1 X 1 X 2 a a b a a a b

Example of MPM Grammar MPMG X 1 = a X 2 = b X

Example of MPM Grammar MPMG X 1 = a X 2 = b X 3 = X 1 X 2 X 4 = X 1 X 5 = X 2 X 1 X 6 = X 2 X 7 = X 3 X 4 X 8 = X 5 X 9 = X 6 X 3 X 10 = X 7 X 8 X 11 = X 9 X 2 X 12 = X 10 X 11 T = abaabababbaba X 12 X 10 X 11 X 7 X 3 X 8 X 4 X 5 X 9 X 5 X 6 X 3 X 1 X 2 X 1 X 2 X 2 a b a b a b a