Reducing the size of NFAs by using equivalences and preorders

Authors:
Lucian Ilie;Roberto Solis-Oba;Sheng Yu
Affiliations:
Department of Computer Science, University of Western Ontario, London, Ontario, Canada;Department of Computer Science, University of Western Ontario, London, Ontario, Canada;Department of Computer Science, University of Western Ontario, London, Ontario, Canada
Venue:
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Year:
2005

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Abstract

The efficiency of regular expression matching algorithms depends very much on the size of the nondeterministic finite automata (NFA) obtained from regular expressions. Reducing the size of these automata by using equivalences has been shown to reduce significantly the search time. We consider the problem of reducing the size of arbitrary NFAs using equivalences and preorders. For equivalences, we give an algorithm to optimally combine equivalent states for reducing the size of the automata. We also show that the problem of optimally using preorders to reduce the size of an automaton is NP-hard.