Nathalie Aubrun

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In this article we study how a subshift can simulate another one, where the notion of simulation is given by operations on subshifts inspired by the dynamical systems theory (factor, projective subaction...). There exists a correspondence between the notion of simulation and the set of forbidden patterns. The main result of this paper states that any(More)
This thesis is devoted to the study of subshifts, or symbolic dynamical systems, defined on some finitely presented monoids like Zd or the infinite binary tree. The main result concerning multidimensional subshifts establishes that any effective subshift of dimension d can be obtained by factor map and projective subaction of a subshift of finite type of(More)
A one-sided (resp. two-sided) shift of finite type of dimension one can be described as the set of infinite (resp. bi-infinite) sequences of consecutive edges in a finite-state automaton. While the conjugacy of shifts of finite type is decidable for one-sided shifts of finite type of dimension one, the result is unknown in the two-sided case. In this paper,(More)
Wang tilings are colorings of the Euclidean plane that respect some local constraints. They can be viewed both as dynamical systems and computational models, but they were first introduced by Hao Wang to study decision problems on some classes of logical formulas [18]. The concept of Wang tiles may be generalized to define tilings on the Cayley graph of a(More)
A Theorem of Gao, Jackson and Seward, originally conjectured to be false by Glasner and Uspenskij, asserts that every countable group admits a 2-coloring. A direct consequence of this result is that every countable group has a strongly aperiodic subshift on the alphabet {0, 1}. In this article, we use Lovász local lemma to first give a new simple proof of(More)