Limit Sets of Stable and Unstable Cellular Automata

Alexis Ballier (1, 2) , Pierre Guillon (3, 2) , Jarkko Kari (2)

1 CMM - Center for Mathematical Modeling
2 FUNDIM - Departement of Mathematics, University of Turku
3 IML - Institut Mathématiques de Luminy

We construct a cellular automaton (CA) with a sofic and mixing limit set and then construct a stable CA with the same limit set, showing there exist subshifts that can be limit sets of both stable and unstable CAs, answering a question raised by A.~Maass.

Domaines: Mathématique discrète [cs.DM]

Alexis Ballier, Pierre Guillon, Jarkko Kari. Limit Sets of Stable and Unstable Cellular Automata. Fundamenta Informaticae, 2011, 110, pp.1--12. ⟨hal-01281010⟩