2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229757We show that a set with an action of a locally finite-dimensional free partially commutative monoid and the corresponding semicubical set have isomorpic homology groups. We build a complex of finite length for the computing homology groups of any asynchronous transition system with finite maximal number of mutually independent events. We give examples of computing the homology groups.21 pagesK-Theory and HomologyAlgebraic Topology18G10; 18G35; 55U10; 68Q10; 68Q85text