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Pré-Publication, Document De Travail Année : 2022

Parametrization by Horizontal Constraints in the Study of Algorithmic Properties of Z^2-Subshift of Finite Type

Solène J. Esnay
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Mathieu Sablik

Résumé

The non-emptiness, called the Domino Problem, and the characterization of the possible entropies of $\mathbb{Z}^2$-subshifts of finite type are standard problems of symbolic dynamics. In this article we study these questions with horizontal constraints fixed beforehand as a parameter. We determine for which horizontal constraints the Domino Problem is undecidable and when all right-recursively enumerable numbers can be obtained as entropy, with two approaches: either the additional local rules added to the horizontal constraints can be of any shape, or they can only be vertical rules.

Dates et versions

hal-03632414 , version 1 (06-04-2022)

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Solène J. Esnay, Mathieu Sablik. Parametrization by Horizontal Constraints in the Study of Algorithmic Properties of Z^2-Subshift of Finite Type. 2022. ⟨hal-03632414⟩
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