Reducing NFAs by invariant equivalences

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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.

Keywords

Non-deterministic finite automata
Regular expressions
Automata minimization
Invariant equivalences
Derivatives of regular expressions

Cited by (0)

An extended abstract of this paper has been presented at The 27th International Symposium on Mathematical Foundations of Computer Science (MFCS’02) (Warsaw, 2002); see [16].

1

Research partially supported by NSERC Grant R3143A01.

2

Research partially supported by NSERC Grant OGP0041630.