Characterizations of periods of multidimensional shifts

Emmanuel Jeandel (1) , Pascal Vanier (2, 3)

1 CARTE - Theoretical adverse computations, and safety
2 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166
3 Einstein Institute of Mathematics

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.

Mots clés: subshift; shift of finite type; complexity; periodicity; periods

Domaines: Mathématique discrète [cs.DM]; Systèmes dynamiques [math.DS]; Complexité [cs.CC]; Logique en informatique [cs.LO]

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