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.

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