4452 articles – 13148 references  [version française]
 HAL: hal-00613165, version 2
 arXiv: 1108.1012
 Available versions: v1 (2011-08-04) v2 (2011-08-25) v3 (2012-06-01)
 Turing degrees of multidimensional SFTs
 (2011-08-03)
 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 $P\times\ZZ^2$ is recursively homeomorphic to $X\setminus U$ 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.
 1: Laboratoire d'informatique Fondamentale de Marseille (LIF) CNRS : UMR6166 – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I
 Subject : Computer Science/Discrete Mathematics
 Keyword(s): Tilings – Subshift of Finite Type – Undecidability – \pizu classes – Turing degree
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 hal-00613165, version 2 http://hal.archives-ouvertes.fr/hal-00613165 oai:hal.archives-ouvertes.fr:hal-00613165 From: Pascal Vanier <> Submitted on: Thursday, 25 August 2011 11:09:01 Updated on: Thursday, 25 August 2011 11:37:52