Reducing NFAs by invariant equivalences

Authors:
Lucian Ilie;Sheng Yu
Affiliations:
Department of Computer Science, University of Western Ontario, London, ON, Canada N6A 5B7;Department of Computer Science, University of Western Ontario, London, ON, Canada N6A 5B7
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

We give new general methods for constructing small non-deterministic finite automata (NFA) from arbitrary ones. Given an NFA, we compute the largest right-invariant equivalence on the set of states and then merge the equivalent states to obtain a smaller automaton. When applying this method to position automata, we get a way to convert regular expressions into NFAs which are always smaller than or equal to the position, partial derivative, and follow automata; it can be arbitrarily smaller. The construction can be dually made for left-invariant equivalences and then the two can be combined for even better results.