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arXiv · 1410.4488

On Torsion-Free Semigroups Generated by Invertible Reversible Mealy Automata

Thibault Godin·Ines Klimann·Matthieu Picantin
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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.

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Thibault Godin, Ines Klimann, Matthieu Picantin. 2014-10-16. On Torsion-Free Semigroups Generated by Invertible Reversible Mealy Automata. https://arxiv.org/abs/1410.4488

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