Rice's theorem for generic limit sets of cellular automata

Martin Delacourt (1, 2)

1 UO - Université d'Orléans
2 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

The generic limit set of a cellular automaton is a topologically dened set of congurations that intends to capture the asymptotic behaviours while avoiding atypical ones. It was dened by Milnor then studied by Djenaoui and Guillon rst, and by Törmä later. They gave properties of this set related to the dynamics of the cellular automaton, and the maximal complexity of its language. In this paper, we prove that every non trivial property of these generic limit sets of cellular automata is undecidable.

Domaines: Mathématique discrète [cs.DM]; Systèmes dynamiques [math.DS]

Martin Delacourt. Rice's theorem for generic limit sets of cellular automata. AUTOMATA 2021, Jul 2021, Marseille, France. ⟨hal-03259515⟩