Test Sets for Finite Substitutions

Abstract Ehrenfeucht's Conjecture, that each subset S of a finitely generated free monoid has a finite subset T such that if two endomorphisms of the monoid agree on T , then they agree on S , has recently been verified. In this paper we extend this result from endomorphisms to certain types of finite substitutions by applying Konig's Lemma, and embeddings of the monoid into a free algebra.