Codes modulo finite monadic string-rewriting systems

AbstractA set C⊆Σ∗ is called a code modulo a string-rewriting system T if, for all v1,v2,…vk, w1,w2,…,wmϵC,v1v2…vk↔*Tw1w2…wm implies that it is decidable whether a regular set is a code modulo T, when T is a finite string-rewriting system that is monadic and confluent, or that is special and λ-confluent