Detecting patterns in finite regular and context-free languages

Authors:
Narad Rampersad;Jeffrey Shallit
Affiliations:
Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Ave., Winnipeg, MB R3B 2E9, Canada;School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Venue:
Information Processing Letters
Year:
2010

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Abstract

We consider some natural variations on the following classic pattern-matching problem: given an NFA M over the alphabet @S and a pattern p over some alphabet @D, does there exist a word x@?L(M) such that x matches p? We consider the restricted problem where M only accepts a finite language. We also consider the variation where only some factor of x is required to match the pattern p. We show that both of these problems are NP-complete. We also consider the same problems for context-free grammars; in this case the problems become PSPACE-complete.