No abstract

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.

Subshifts are shift invariant closed subsets of Σ Z d , minimal subshifts are subshifts in which all points contain the same patterns. It has been proved by Jeandel and Vanier that the Turing degree spectra of nonperiodic minimal subshifts always contain the cone of Turing degrees above any of its degree. It was however not known whether each minimal subshift's spectrum was formed of exactly one cone or not. We construct inductively a minimal subshift whose spectrum consists of an uncountable number of cones with disjoint base.