Recognizability in S-adic shifts
Marie-Pierre Béal, Dominique Perrin, Antonio Restivo, Wolfgang Steiner · arXiv (Cornell University) · 2023
We investigate questions related to the notion of recognizability of sequences of morphisms, a generalization of Moss{é}'s Theorem. We consider the most general class of morphisms including ones with erasable letters. The main result states that a sequence of morphisms with finite alphabet rank is eventually recognizable for aperiodic points, improving and simplifying a result of Berth{é} et al. (2019). This also provides a new simple proof for the recognizability of a single morphism on its shift space. The main ingredient of the proof are elementary morphisms.