On regularity of languages generated by copying systems

Abstract Let Σ be an arbitrary fixed alphabet. The direct copying relation (over Σ+) is a binary relation defined by: x copy y if and only if x = x1ux2 and y = x1uux2 for some words x1,x2,u where u is nonempty. The copying relation copy∗ is defined as the reflexive and transitive closure of copy. A copying system is an ordered pair G = (Σ, w) where w ϵΣ+; its language is L(G) = {zϵΣ + : w copy ∗ z} , it is referred to as a copy language. This note provides a sufficient condition for a copy language to be regular; an application of this condition is demonstrated.