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Conference Papers Year : 2023

Sturmian and infinitely desubstitutable words accepted by an ω-automaton

Mots Sturmiens et infiniment désubstituables acceptés par un ω-automate

Abstract

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

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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⟩
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