When are dual Cayley automaton semigroups finite?

Abstract

In this note we prove that, for a finite semigroup $S$, the dual Cayley automaton semigroup ${\mathbf{C}}^{\ast }(S)$ is finite if and only if $S$ is $\mathcal{H}$-trivial and has no non-trivial right zero subsemigroups.

6 pages, 1 figure