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arXiv · 1801.10009

Infinite finitely generated automata semigroups have infinite orbits

Dominik Francoeur
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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.

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Dominik Francoeur. 2018-01-30. Infinite finitely generated automata semigroups have infinite orbits. https://arxiv.org/abs/1801.10009

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