Parametrization by Horizontal Constraints in the Study of Algorithmic Properties of $\mathbb{Z}^2$-Subshift of Finite Type
Dynamical Systems
2024-10-07 v2
Abstract
The non-emptiness, called the Domino Problem, and the characterization of the possible entropies of -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.
Keywords
Cite
@article{arxiv.2203.00434,
title = {Parametrization by Horizontal Constraints in the Study of Algorithmic Properties of $\mathbb{Z}^2$-Subshift of Finite Type},
author = {Solène J. Esnay and Mathieu Sablik},
journal= {arXiv preprint arXiv:2203.00434},
year = {2024}
}