A note on decidability questions on presentations of word semigroups

AbstractWe apply automata-theoretic tools and some recently established compactness properties in the study of F-rmsemigroups, that is, subsemigroups of free semigroups. With each F-semigroup we associate an F-presentation, which turns out to be finite for all finitely generated F-semigroups. Connections between F-presentations and ordinary presentations of semigroups are pointed out. It is also shown that it is undecidable whether two finitely generated F-semigroups satisfy a common relation in their F-presentations