A new regular grammar pattern matching algorithm

This paper presents a Boyer–Moore type algorithm for regular grammar pattern matching, answering a variant of an open problem posed by Aho (Pattern Matching in Strings, Academic Press, New York, 1980, p. 342). The new algorithm handles patterns specified by regular (left linear) grammars—a generalization of the Boyer–Moore (single keyword) and Commentz-Walter (multiple keyword) algorithms. Like the Boyer–Moore and Commentz-Walter algorithms, the new algorithm makes use of shift functions which can be precomputed and tabulated. The precomputation functions are derived, and it is shown that they can be obtained from Commentz-Walter's d1 and d2 shift functions. In most cases, the Boyer–Moore (respectively, Commentz-Walter) algorithm has greatly outperformed the Knuth–Morris–Pratt (respectively, Aho–Corasick) algorithm. In practice, an earlier version of the algorithm presented in this paper also frequently outperforms the regular grammar generalization of the Aho–Corasick algorithm.