A Four Russians algorithm for regular expression pattern matching

Authors:
Gene Myers
Affiliations:
The University of Arizona, Tuscon, Arizona
Venue:
Journal of the ACM (JACM)
Year:
1992

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Abstract

Given a regular expression R of length P and a word A of length N, the membership problem is to determine if A is in the language denoted by R. An O(PN/lgN) time algorithm is presented that is based on a lgN speedup of the standard O(PN) time simulation of R's nonderministic finite automaton on A using a combination of the node-listing and “Four-Russians” paradigms. This result places a new worst-case upper bound on regular expression pattern matching. Moreover, in practice the method provides an implementation that is faster than existing software for small regular expressions.