Turing Degree Spectra of Minimal Subshifts

  • Michael Hochman
  • Pascal VanierEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10304)


Subshifts are shift invariant closed subsets of \(\varSigma ^{\mathbb {Z}^d}\), with \(\varSigma \) a finite alphabet. 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 non-periodic minimal subshifts always contain the cone of Turing degrees above any of its degrees. 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 incomparable bases.


Turing Machine Finite Type Computable Point Finite Alphabet Turing Degree 
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Authors and Affiliations

  1. 1.Einstein Institute of MathematicsHebrew University of JerusalemJerusalemIsrael
  2. 2.Laboratoire d’Algorithmique, Complexité et Logique, Université de Paris-Est, LACL, UPECCréteilFrance

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