Communication Complexity and Intrinsic Universality in Cellular Automata - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2009

Communication Complexity and Intrinsic Universality in Cellular Automata

Résumé

The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce necessary conditions for a cellular automaton to be "universal", according to a precise notion of simulation, related both to the dynamics of cellular automata and to their computational power. This notion of simulation relies on simple operations of space-time rescaling and it is intrinsic to the model of cellular automata. Intrinsinc universality, the derived notion, is stronger than Turing universality, but more uniform, and easier to define and study. Our approach builds upon the notion of communication complexity, which was primarily designed to study parallel programs, and thus is, as we show in this article, particulary well suited to the study of cellular automata: it allowed to show, by studying natural problems on the dynamics of cellular automata, that several classes of cellular automata, as well as many natural (elementary) examples, could not be intrinsically universal.
Fichier principal
Vignette du fichier
main.pdf (337.17 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00440186 , version 1 (09-12-2009)
hal-00440186 , version 2 (01-02-2010)
hal-00440186 , version 3 (30-08-2010)
hal-00440186 , version 4 (15-09-2010)

Identifiants

Citer

Eric Goles Chacc, Pierre-Etienne Meunier, Ivan Rapaport, Guillaume Theyssier. Communication Complexity and Intrinsic Universality in Cellular Automata. 2009. ⟨hal-00440186v4⟩
221 Consultations
194 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More