2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75431We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class including groups, such an automaton accepts the word problem of a group H if and only if H has a finite index subgroup which embeds in the group of units of M. In the case that M is a group, this answers a question of Elston and Ostheimer.8 pages, fixed some typos and clarified ambiguity in the abstract, results unchangedGroup Theory20F10 (Primary); 20M05 (Secondary)text