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arXiv · 1208.6324

The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable

Ines Klimann
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Abstract

We prove that a semigroup generated by a reversible two-state Mealy automaton is either finite or free of rank 2. This fact leads to the decidability of finiteness for groups generated by two-state or two-letter invertible-reversible Mealy automata and to the decidability of freeness for semigroups generated by two-state invertible-reversible Mealy automata.

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Ines Klimann. 2013-10-22. The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable. https://doi.org/10.4230/lipics.stacs.2013.502

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