Abstract

Given a sequence A of length M and a regular expression R of length P , an approximate regular expression pattern matching algorithm computes the score of the optimal alignment between A and one of the sequences B exactly matched by R. An alignment between sequences A = a 1 a 2 : : : aM and B = b 1 b 2 : : : b N is a list of ordered pairs, !(i 1 ; j 1 ); (i 2 ; j 2 ); : : : (i t ; j t )? such that i k ! i k+1 and j k ! j k+1 . In this case, the alignment aligns symbols a i k and b jk , and leaves blocks of unaligned symbols, or gaps, between them. A scoring scheme S associates costs for each aligned symbol pair and each gap. The alignment's score is the sum of the associated costs, and an optimal alignment is one of minimal score. There are a variety of schemes for scoring alignments. In a concave gap-penalty scoring scheme S = fffi; wg, a function ffi (a; b) gives the score of each aligned pair of symbols a and b, and a concave function w(k) gives the score of a gap of lengt...

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