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On the languages accepted by finite reversible automata

  • J. E. Pin
Formal Languages And Automata
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)

Abstract

A reversible automaton is a finite (possibly incomplete) automaton in which each letter induces a partial one-to-one map from the set of states into itself. We give four non-trivial characterizations of the languages accepted by a reversible automaton equipped with a set of initial and final states and we show that one can effectively decide whether a given rational (or regular) language can be accepted by a reversible automaton. The first characterization gives a description of the subsets of the free group accepted by a reversible automaton that is somewhat reminiscent of Kleene's theorem. The second characterization is more combinatorial in nature. The decidability follows from the third — algebraic — characterization. The last and somewhat unexpected characterization is a topological description of our languages that solves an open problem about the finite-group topology of the free monoid.

Keywords

Finite Group Inverse Semigroup Topological Description Membership Problem Finite Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • J. E. Pin
    • 1
  1. 1.LITP, University Paris VI and CNRSParis Cedex 05France

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