Decidable problems in substitution shifts

In this paper, we investigate the structure of the most general kind of substitution shifts, including non-minimal ones, and allowing erasing morphisms. We prove the decidability of many properties of these morphisms with respect to the shift space generated by iteration, such as aperiodicity, recog...

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Main Authors Béal, Marie-Pierre, Perrin, Dominique, Restivo, Antonio
Format Journal Article
LanguageEnglish
Published 29.12.2021
Subjects
Computer Science - Formal Languages and Automata Theory
Mathematics - Dynamical Systems
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Abstract In this paper, we investigate the structure of the most general kind of substitution shifts, including non-minimal ones, and allowing erasing morphisms. We prove the decidability of many properties of these morphisms with respect to the shift space generated by iteration, such as aperiodicity, recognizability and (under an additional assumption) irreducibility, or minimality.
AbstractList In this paper, we investigate the structure of the most general kind of substitution shifts, including non-minimal ones, and allowing erasing morphisms. We prove the decidability of many properties of these morphisms with respect to the shift space generated by iteration, such as aperiodicity, recognizability and (under an additional assumption) irreducibility, or minimality.
Author Béal, Marie-Pierre
Restivo, Antonio
Perrin, Dominique
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BackLink https://doi.org/10.48550/arXiv.2112.14499$$DView paper in arXiv
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Snippet In this paper, we investigate the structure of the most general kind of substitution shifts, including non-minimal ones, and allowing erasing morphisms. We...
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SubjectTerms Computer Science - Formal Languages and Automata Theory
Mathematics - Dynamical Systems
Title Decidable problems in substitution shifts
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