On Torsion-Free Semigroups Generated by Invertible Reversible Mealy Automata

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8977)

Abstract

This paper addresses the torsion problem for a class of automaton semigroups, defined as semigroups of transformations induced by Mealy automata, aka letter-by-letter transducers with the same input and output alphabet. The torsion problem is undecidable for automaton semigroups in general, but is known to be solvable within the well-studied class of (semi)groups generated by invertible bounded Mealy automata. We focus on the somehow antipodal class of invertible reversible Mealy automata and prove that for a wide subclass the generated semigroup is torsion-free.

Keywords

Automaton semigroup Reversible mealy automaton   Labeled orbit tree Torsion-free semigroup 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Thibault Godin
    • 1
  • Ines Klimann
    • 1
  • Matthieu Picantin
    • 1
  1. 1.Université Paris Diderot, Sorbonne Paris Cité, LIAFA, UMR 7089 CNRSParisFrance

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