# Characterizations of periods of multidimensional shifts

1 CARTE - Theoretical adverse computations, and safety
LORIA - FM - Department of Formal Methods , Inria Nancy - Grand Est
Abstract : We show that the sets of periods of multidimensional shifts of finite type (SFTs) are exactly the sets of integers of the complexity class $\NE$. We also show that the functions counting their number are the functions of $\#\E$. We also give characterizations of some other notions of periodicity. We finish the paper by giving some characterizations for sofic and effective subshifts.
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Cited literature [18 references]

https://hal.archives-ouvertes.fr/hal-00798336
Contributor : Pascal Vanier <>
Submitted on : Friday, March 8, 2013 - 1:28:23 PM
Last modification on : Tuesday, December 18, 2018 - 4:48:02 PM
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### Citation

Emmanuel Jeandel, Pascal Vanier. Characterizations of periods of multidimensional shifts. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2015, 35 (2), pp.431--460. ⟨10.1017/etds.2013.60⟩. ⟨hal-00798336⟩

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