1D Effectively Closed Subshifts and 2D Tilings

Bruno Durand (1) , Andrei Romashchenko (1) , Alexander Shen (1)

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

Michael Hochman showed that every 1D effectively closed subshift can be simulated by a 3D subshift of finite type and asked whether the same can be done in 2D. It turned out that the answer is positive and necessary tools were already developed in tilings theory. We discuss two alternative approaches: first, developed by N. Aubrun and M. Sablik, goes back to Leonid Levin; the second one, developed by the authors, goes back to Peter Gacs.

Keywords: effectively closed subshifts; subshifts of finite type; tilings

Domains: Other [cs.OH]

Bruno Durand, Andrei Romashchenko, Alexander Shen. 1D Effectively Closed Subshifts and 2D Tilings. Journées Automates Cellulaires, Dec 2010, Turku, Finland. pp.2-7. ⟨hal-00541881⟩