Turing degrees of multidimensional subshifts
Résumé
In this paper we are interested in computability aspects of subshifts and in particular Turing degrees of 2-dimensional SFTs (i.e. tilings). To be more precise, we prove that given any \pizu subset P of {0,1}\NN there is a SFT X such that P×\ZZ2 is recursively homeomorphic to X∖U where U is a computable set of points. As a consequence, if P contains a recursive member, P and X have the exact same set of Turing degrees. On the other hand, we prove that if X contains only non-recursive members, some of its members always have different but comparable degrees. This gives a fairly complete study of Turing degrees of SFTs.
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