The co-word problem for the Higman-Thompson group is context-free
Jörg Lehnert, Pascal Schweitzer · Bulletin of the London Mathematical Society · 2007
The 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 show that a permutation group has context-free co-word problem. This method is used 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 have an easier co-word problem. We call this property semi-deterministic context-free. The second Houghton group belongs to this class.