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Characterizations of periods of multi-dimensional shifts

Published online by Cambridge University Press:  27 September 2013

EMMANUEL JEANDEL  and
PASCAL VANIER
EMMANUEL JEANDEL
Affiliation:
LORIA, Campus Scientifique, BP 239, 54506 Vandoeuvre-lès-Nancy, France email emmanuel.jeandel@loria.fr
PASCAL VANIER
Affiliation:
Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel email pascal.vanier@ens-lyon.org
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Abstract

We show that the sets of periods of multi-dimensional shifts of finite type are precisely the sets of integers of the complexity class NP. We also show that the functions counting their number are the functions of #P. We also give characterizations of some other notions of periodicity in terms of space complexity. We finish the paper by giving some characterizations for sofic and effective subshifts.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 2 , April 2015 , pp. 431 - 460
Copyright
© Cambridge University Press, 2013 

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