Computational Complexity of Avalanches in the Kadanoff two-dimensional Sandpile Model

15 pagesIn this paper we prove that the avalanche problem for Kadanoff sandpile model (KSPM) is P-complete for two-dimensions. Our proof is based on a reduction from the monotone circuit value problem by building logic gates and wires which work with configurations in KSPM. The proof is also related to the known prediction problem for sandpile which is in NC for one-dimensional sandpiles and is P-complete for dimension 3 or greater. The computational complexity of the prediction problem remains open for two-dimensional sandpiles

Communication Complexity and Intrinsic Universality in Cellular Automata

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

Comportement oscillatoire d'une famille d'automates cellulaires non uniformes

Universités : Université scientifique et médicale de Grenoble et Institut national polytechnique de Grenobl

Comportement dynamique de réseaux d'automates

Université : Université scientifique et médicale de GrenobleCette thèse rassemble plusieurs articles ayant pour sujet l'étude de la dynamique d'une large classe de réseaux d'automates. Deux outils sont introduits: les invariants algébriques associés à l'évolution temporelle; la fonction d'énergie permettant de déterminer l'évolution du réseau, tant en régime transitoire qu'en régime stationnaire. Finalement, nous étudions des réseaux unidimensionnels, la dynamique d'un automate à mémoire et les réseaux des fonctions booléennes à deux variable

Comportement oscillatoire d'une famille d'automates cellulaires non uniformes

Universités : Université scientifique et médicale de Grenoble et Institut national polytechnique de Grenobl