Sturmian and infinitely desubstitutable words accepted by an ω-automaton - Graphes, Algorithmes et Combinatoire
Communication Dans Un Congrès Année : 2023

Sturmian and infinitely desubstitutable words accepted by an ω-automaton

Mots Sturmiens et infiniment désubstituables acceptés par un ω-automate

Résumé

Given an ω-automaton and a set of word homomorphisms, we look at which accepted words have such a substitutive structure, and in particular if there is at least one. We introduce a method using desubstitution of ω-automata to describe the structure of preimages of accepted words under arbitrary sequences of homomorphisms: this takes the form of a meta-ω-automaton. We decide the existence of an accepted purely substitutive word, as well as the existence of an accepted fixed point. In the case of multiple substitutions (non-erasing homomorphisms), we decide the existence of an accepted infinitely desubstitutable word, with possibly some constraints on the sequence of substitutions (e.g. Sturmian words or Arnoux-Rauzy words). As an application, we decide when a set of finite words codes e.g. a Sturmian word. As another application, we also show that if an ω-automaton accepts a Sturmian word, it accepts the image of the full shift under some Sturmian morphism.
Fichier principal
Vignette du fichier
hal.pdf (362.33 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04034705 , version 1 (17-03-2023)

Licence

Identifiants

Citer

Pierre Béaur, Benjamin Hellouin de Menibus. Sturmian and infinitely desubstitutable words accepted by an ω-automaton. WORDS 2023, Martin Berglund; Johanna Björklund; Frank Drewes; Lena Strobl, Jun 2023, Umeå, Sweden. ⟨10.1007/978-3-031-33180-0_8⟩. ⟨hal-04034705⟩
213 Consultations
45 Téléchargements

Altmetric

Partager

More