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A Characterization of Those Automata That Structurally Generate Finite Groups

  • Ines Klimann
  • Matthieu Picantin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)

Abstract

Antonenko and Russyev independently have shown that any Mealy automaton with no cycle with exit—that is, where every cycle in the underlying directed graph is a sink component—generates a finite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper.

Keywords

automaton groups Mealy automata finiteness problem 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ines Klimann
    • 1
  • Matthieu Picantin
    • 1
  1. 1.Sorbonne Paris Cité, LIAFA, UMR 7089 CNRSUniv Paris DiderotParisFrance

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