On the equivalence of compositions of morphisms and inverse morphisms on regular languages

Abstract

We establish as our main results the following two theorems on compositions of morphisms and inverse morphisms. It is undecidable whether or not two transductions of the form h2h 2 −1 , where h1 and h2 are morphisms, are equivalent (word by word) on a given regular language, while the same problem for transductions of the form h 1 −1 h2 is decidable. Consequently, a sharp borderline between decidable and undecidable problems is found.