Monadic Thue Systems

Certain infinite Thue systems over a finite alphabet are studied, in particular, systems S⊆∑∗×(∑∪{e}) such that for each aϵ∑∪{e}, the set {u| (u,a)ϵS} is a context-freelanguage. The syntactic structure of sets of ancestors and sets of descendants is considered, as well as that of unions of congruence classes, taken over (infinite) context-free languages or regular sets. The common descendant problem is shown to be tractable while the common ancestor problem is shown to be undecidable (even for finite systems). The word problem for confluent systems of this type is shown to be tractable. The question of whether an infinite system of this type is confluent is shown to be undecidable as is the question of whether the congruence generated by such a system has a confluent presentation.