2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122899We describe in terms of automata theory the automatic actions with post-critically finite limit space. We prove that these actions are precisely the actions by bounded automata and that any self-similar action by bounded automata is contracting.13 pagesGroup TheoryMetric Geometry20E08; 28A80; 39A12text