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Decidability of the isomorphism and the factorization between minimal substitution subshifts

Abstract : Classification is a central problem for dynamical systems, in particular for families that arise in a wide range of topics, like substitution subshifts. It is important to be able to distinguish whether two such subshifts are isomorphic, but the existing invariants are not sufficient for this purpose. We first show that given two minimal substitution subshifts, there exists a computable constant R such that any factor map between these sub-shifts (if any) is the composition of a factor map with a radius smaller than R and some power of the shift map. Then we prove that it is decid-able to check whether a given sliding block code is a factor map between two prescribed minimal substitution subshifts. As a consequence of these two results, we provide an algorithm that, given two minimal substitution subshifts, decides whether one is a factor of the other and, as a straightforward corollary, whether they are isomorphic.
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Contributeur : Fabien Durand Connectez-vous pour contacter le contributeur
Soumis le : jeudi 11 août 2022 - 17:41:58
Dernière modification le : mercredi 9 novembre 2022 - 13:42:09


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  • HAL Id : hal-02461469, version 2
  • ARXIV : 1806.04891



Fabien Durand, Julien Leroy. Decidability of the isomorphism and the factorization between minimal substitution subshifts. Discrete Analysis, 2022. ⟨hal-02461469v2⟩



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