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- Nathalie Aubrun, Mathieu Sablik
- ArXiv
- 2011

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)

- Nathalie Aubrun, Marie-Pierre Béal
- CSR
- 2010

We introduce the notion of sofic tree-shifts which corresponds to symbolic dynamical systems of infinite trees accepted by finite tree automata. We show that, contrary to shifts of infinite sequences, there is no unique minimal deterministic irreducible tree automaton accepting an irreducible sofic tree-shift, but that there is a unique synchronized one,… (More)

- Nathalie Aubrun, Marie-Pierre Béal
- ICALP
- 2009

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)

- Nathalie Aubrun, Sebastián Barbieri, Mathieu Sablik
- Theor. Comput. Sci.
- 2017

We define a notion of effectiveness for subshifts on finitely generated groups. The set of effective subshifts forms a conjugacy class that contains the class of sofic subshifts. We prove that the inclusion is strict for several groups, including amenable groups and groups with more than two ends.

- Nathalie Aubrun
- 2011

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)

- Nathalie Aubrun, Marie-Pierre Béal
- Theor. Comput. Sci.
- 2012

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)

- Nathalie Aubrun, Mathieu Sablik
- STACS
- 2009

Traditionally a tiling is defined with a finite number of finite forbidden patterns. We can generalize this notion considering any set of patterns. Generalized tilings defined in this way can be studied with a dynamical point of view, leading to the notion of subshift. In this article we establish a correspondence between an order on subshifts based on… (More)

- Nathalie Aubrun, Jarkko Kari
- MCU
- 2013

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)

- Nathalie Aubrun, Mathieu Sablik
- ArXiv
- 2011

In this article we prove that multidimensional effective Sadic systems, obtained by applying an effective sequence of substitutions chosen among a finite set of substitutions, are sofic subshifts.

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)