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Characterizations of periods of multi-dimensional shifts

Published online by Cambridge University Press:  27 September 2013

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

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
Copyright
© Cambridge University Press, 2013 

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