Abstract

. This paper analyzes the expected performance of a simplified version BM 0 of the Boyer--Moore string matching algorithm. A probabilistic automaton A is set up which models the expected behavior of BM 0 under the assumption that both text and pattern are generated by a source which emits independent and uncorrelated symbols with an arbitrary distribution of probabilities. Formal developments lead then to the conclusion that A takes expected sublinear time in a variety of situations. The sublinear behavior can be quantitatively predicted by simple formulae involving the pattern length m and the alphabet's probabilistic properties. Finally, empirical evidence is provided which is in satisfactory accordance with the theory. Keywords : String searching, Pattern matching, Average case analysis of algorithms. 1 1 The problem Let A be a finite alphabet, jAj =: n, and suppose strings T = t 1 :::t N ; t i 2A; 1iN (the "text 00 ) S = s 1 :::s m ; s i 2A; 1imN (the "pattern 00 ) are...

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