We prove that the semigroup generated by a reversible Mealy automaton contains a free subsemigroup of rank two if and only if it contains an element of infinite order.
Cite this article
Dominik Francoeur, Ivan Mitrofanov, On the existence of free subsemigroups in reversible automata semigroups. Groups Geom. Dyn. 15 (2021), no. 3, pp. 1103–1132DOI 10.4171/GGD/626