Infinite finitely generated automata semigroups have infinite orbits

Abstract

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

8 pages, 4 figures

References in corpus (1)

• The smallest Mealy automaton of intermediate growth