Infinite finitely generated automata semigroups have infinite orbits
classification
🧮 math.GR
keywords
infinitegeneratedalphabetautomataautomatonexistsfinitefinitely
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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.
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