English

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}
}
R2 v1 2026-06-28T08:38:36.708Z