An Order on Sets of Tilings Corresponding to an Order on Languages

Nathalie Aubrun (1) , Mathieu Sablik (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

Traditionally a tiling is defined with a finite number of finite forbidden patterns. We can generalize this notion considering any set of patterns. Generalized tilings defined in this way can be studied with a dynamical point of view, leading to the notion of subshift. In this article we establish a correspondence between an order on subshifts based on dynamical transformations on them and an order on languages of forbidden patterns based on computability properties.

Mots clés: tiling; subshift; Turing machine with oracle; subdynamics

Domaines: Mathématique discrète [cs.DM]

Nathalie Aubrun, Mathieu Sablik. An Order on Sets of Tilings Corresponding to an Order on Languages. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. pp.99-110. ⟨inria-00359625⟩