Recognizability in S-adic shifts
Formal Languages and Automata Theory
2023-12-14 v2 Dynamical Systems
Abstract
We investigate questions related to the notion of recognizability of sequences of morphisms, a generalization of Moss{\'e}'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{\'e} 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.
Keywords
Cite
@article{arxiv.2302.06258,
title = {Recognizability in S-adic shifts},
author = {Marie-Pierre Béal and Dominique Perrin and Antonio Restivo and Wolfgang Steiner},
journal= {arXiv preprint arXiv:2302.06258},
year = {2023}
}