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Pré-Publication, Document De Travail Année : 2023

Recognizability in S-adic shifts

Résumé

We investigate questions related to the notion of recognizability of sequences of morphisms, a generalization of Mossé'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 bounded alphabet size is eventually recognizable for aperiodic points, improving and simplifying a result of Berthé 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.
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Dates et versions

hal-03983501 , version 1 (10-02-2023)
hal-03983501 , version 2 (11-12-2023)

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Marie-Pierre Béal, Dominique Perrin, Antonio Restivo, Wolfgang Steiner. Recognizability in S-adic shifts. 2023. ⟨hal-03983501v1⟩

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