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The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable
Published 30 Aug 2012 in cs.FL and math.GR | (1208.6324v2)
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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