HAL: hal-00613165, version 2

arXiv: 1108.1012

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Turing degrees of multidimensional SFTs

Emmanuel Jeandel 1, Pascal Vanier 1

(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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From: Pascal Vanier <>

Submitted on: Thursday, 25 August 2011 11:09:01

Updated on: Thursday, 25 August 2011 11:37:52