Pi01 sets and tilings

Emmanuel Jeandel (1) , Pascal Vanier (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

In this paper, we prove that given any $\Pi^0_1$ subset $P$ of $\{0,1\}^\NN$ there is a tileset $\tau$ with a set of configurations $C$ such that $P\times\ZZ^2$ is recursively homeomorphic to $C\setminus U$ where $U$ is a computable set of configurations. As a consequence, if $P$ is countable, this tileset has the exact same set of Turing degrees.

Mots clés: Tilings; Pi01 sets; computability; SFT

Domaines: Mathématique discrète [cs.DM]

Emmanuel Jeandel, Pascal Vanier. Pi01 sets and tilings. Theory and Applications of Models of Computation - 8th Annual Conference, May 2011, Kyoto, Japan. pp.230-239, ⟨10.1007/978-3-642-20877-5_24⟩. ⟨hal-00563458v2⟩