Bideterministic automata and minimal representations of regular languages

Authors:
Hellis Tamm;Esko Ukkonen
Affiliations:
Department of Computer Science, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland;Department of Computer Science, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland
Venue:
Theoretical Computer Science - Implementation and application of automata
Year:
2004

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Abstract

Bideterministic automata are deterministic automata with the property of their reversal automata also being deterministic. It has been known that a bideterministic automaton is the minimal deterministic automaton accepting its language. This paper shows that any bideterministic automaton is the unique minimal automaton among all (including nondeterministic) automata accepting the same language. We also present a more general result that shows that under certain conditions a minimal deterministic automaton accepting some language or the reversal of the minimal deterministic automaton of the reversal language is a minimal automaton representation of the language. These conditions can be checked in polynomial time.