2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166057In 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 figureGroup Theory20M10text