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The expressiveness of quasiperiodic and minimal shifts of finite type

Published online by Cambridge University Press:  22 January 2020

BRUNO DURAND
Affiliation:
LIRMM, Université Montpellier, Computer Science, Montpellier, France email bruno.durand@lirmm.fr, andrei.romashchenko@lirmm.fr
ANDREI ROMASHCHENKO
Affiliation:
LIRMM, Université Montpellier, Computer Science, Montpellier, France email bruno.durand@lirmm.fr, andrei.romashchenko@lirmm.fr
Corresponding

Abstract

We study multidimensional minimal and quasiperiodic shifts of finite type. We prove for these classes several results that were previously known for the shifts of finite type in general, without restriction. We show that some quasiperiodic shifts of finite type admit only non-computable configurations; we characterize the classes of Turing degrees that can be represented by quasiperiodic shifts of finite type. We also transpose to the classes of minimal/quasiperiodic shifts of finite type some results on subdynamics previously known for effective shifts without restrictions: every effective minimal (quasiperiodic) shift of dimension $d$ can be represented as a projection of a subdynamics of a minimal (respectively, quasiperiodic) shift of finite type of dimension $d+1$ .

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Original Article
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© The Author(s) 2020. Published by Cambridge University Press

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