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Infinite finitely generated automata semigroups have infinite orbits

Published 30 Jan 2018 in math.GR | (1801.10009v1)

Abstract: We prove that the semigroup generated by a finite state Mealy automaton A=(Q,A,Ï„)\mathcal{A}=(Q,A,\tau) is infinite if and only if there exists some right-infinite word in the alphabet AA with infinite orbit.

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