Rice's Theorem for µ-Limit Sets of Cellular Automata

Martin Delacourt (1)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

Cellular automata are a parallel and synchronous computing model, made of innitely many nite automata updating according to the same local rule. Rice's theorem states that any nontrivial property over computable functions is undecidable. It has been adapted by Kari to limit sets of cellular automata [Kar94], that is the set of congurations that can be reached arbitrarily late. This paper proves a new Rice theorem for µ-limit sets, which are sets of congurations often reached arbitrarily late.

Domaines: Mathématique discrète [cs.DM]; Théorie de l'information [cs.IT]; Systèmes dynamiques [math.DS]

Martin Delacourt. Rice's Theorem for µ-Limit Sets of Cellular Automata. Luca Aceto, Monika Henzinger, Jiří Sgall. Automata, Languages and Programming, 6756, Springer, pp.89-100, 2011, Lecture Notes in Computer Science, ⟨10.1007/978-3-642-22012-8_6⟩. ⟨hal-01957552⟩