Recognizability of morphisms

TL;DR

This paper provides a new proof and generalization of Mossé's theorem on recognizable morphisms, extending results to non-primitive and erasable letter morphisms, and offers methods to decide recognizability for injective morphisms.

Contribution

It introduces a new proof of Mossé's theorem, generalizes it to broader classes of morphisms including erasable letters, and presents a decision procedure for recognizability of injective morphisms.

Findings

New proof of Mossé's theorem

Generalization to non-primitive morphisms with erasable letters

Decidability of recognizability for injective morphisms

Abstract

We investigate several questions related to the notion of recognizable morphism. The main result is a new proof of Moss\'e's theorem and actually of a generalization to non primitive morphisms due to Berth\'e et al. We actually prove the result of Berth\'e et al. for the most general class of morphisms, including ones with erasable letters. It is derived from a result concerning elementary morphisms for which we also provide a new proof. We also show how to decide whether an injective morphism is recognizable on the full shift for aperiodic points.