Parametrization by horizontal constraints in the study of algorithmic properties of $ \mathbb{Z}^2 $-subshifts of finite type
Solène J. Esnay, Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, F-31062, Toulouse Cedex 9, France, Mathieu Sablik · Discrete and Continuous Dynamical Systems · 2023
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.