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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01275179
Contributor : Mathieu Sablik Connect in order to contact the contributor
Submitted on : Wednesday, February 17, 2016 - 12:45:07 AM
Last modification on : Tuesday, October 19, 2021 - 10:49:55 PM
Long-term archiving on: : Wednesday, May 18, 2016 - 1:16:32 PM

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

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