2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75679The co-word problem of a group G generated by a set X is defined as the set of words in X which do not represent 1 in G. We introduce a new method to decide if a permutation group has context-free co-word problem. We use this method to show, that the Higman-Thompson groups, and therefore the Houghton groups, have context-free co-word problem. We also give some examples of groups, that even have an easier co-word problem. We call this property semi-deterministic context-free. The second Houghton group belongs to this class.9 pagesGroup Theory20F10; 68Q45 (primary) 03D40 (secondary)text