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Article Dans Une Revue Acta Applicandae Mathematicae Année : 2013

Simulation of Effective Subshifts by Two-dimensional Subshifts of Finite Type

Résumé

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 effective subshift of dimension d – that is a subshift whose set of forbidden patterns can be generated by a Turing machine – can be obtained by applying dynamical operations on a subshift of finite type of dimension d + 1 – a subshift that can be defined by a finite set of forbidden patterns. This result improves Hochman's [Hoc09].
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Dates et versions

hal-01275179 , version 1 (17-02-2016)

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Nathalie Aubrun, Mathieu Sablik. Simulation of Effective Subshifts by Two-dimensional Subshifts of Finite Type. Acta Applicandae Mathematicae, 2013, ⟨10.1007/s10440-013-9808-5⟩. ⟨hal-01275179⟩
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