In this paper we are interested in computability aspects of subshifts and in particular Turing degrees of 2-dimensional SFTs (i.e. tilings). To be more precise, we prove that given any Î 1 class P ofâ€¦ (More)

We show that the sets of periods of multidimensional shifts of finite type (SFTs) are exactly the sets of integers of the complexity class NE. We also show that the functions counting their numberâ€¦ (More)

Tilings and tiling systems are an abstract concept that arise both as a computational model and as a dynamical system. In this paper, we characterize the sets of periods that a tiling system canâ€¦ (More)

Subshifts of finite type are sets of colorings of the plane defined by local constraints. They can be seen as a discretization of continuous dynamical systems. We investigate here the hardness ofâ€¦ (More)

In this paper we study the directions of periodicity of threedimensional subshifts of finite type (SFTs) and in particular their slopes. A configuration of a subshift has a slope of periodicity if itâ€¦ (More)

Cellular automata (CA) are discrete, homogeneous dynamical systems. Non-surjective one-dimensional CA have nite words with no preimage (called orphans), pairs of di erent words starting and endingâ€¦ (More)

Subshifts of finite type are sets of colorings of the plane defined by local constraints. They can be seen as a discretization of continuous dynamical systems. We investigate here the hardness ofâ€¦ (More)

This article studies the complexity of the word problem in groups of automorphisms of subshifts. We show in particular that for any Turing degree, there exists a subshift whose automorphism groupâ€¦ (More)