2 citations · 6 across the 12 of their papers we have counts for
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Pimp my fixpoint: sofic realization of multidimensional substitution-based shift spaces
Antonin Callard, Pierre Guillon, Léo Paviet Salomon +1
In symbolic dynamics, the fixed-point construction from arXiv:0910.2415 defines shift spaces of finite type whose configurations embed infinite hierarchies of tilings. This article…
Decision problems on geometric tilings
Benjamin Hellouin de Menibus, Victor Lutfalla, Pascal Vanier
We study decision problems on geometric tilings. First, we study a variant of the Domino problem where square tiles are replaced by geometric tiles of arbitrary shape. We show that…
Computability of extender sets in multidimensional subshifts: asymptotic growths, dynamical constraints
Antonin Callard, Léo Paviet Salomon, Pascal Vanier
Subshifts are sets of colorings of defined by families of forbidden patterns. In a given subshift, the extender set of a finite pattern is the set of all its admissi…
The relationship between word complexity and computational complexity in subshifts
Ronnie Pavlov, Pascal Vanier
We prove several results about the relationship between the word complexity function of a subshift and the set of Turing degrees of points of the subshift, which we call the Turing…
Slopes of 3-dimensional Subshifts of Finite Type
Etienne Moutot, Pascal Vanier
In this paper we study the directions of periodicity of three-dimensional subshifts of finite type (SFTs) and in particular their slopes. A configuration of a subshift has a slope…
Aperiodic points in -subshifts
Anael Grandjean, Benjamin Hellouin de Menibus, Pascal Vanier
We consider the structure of aperiodic points in -subshifts, and in particular the positions at which they fail to be periodic. We prove that if a -subshi…