Reliable computation with cellular automata
Journal of Computer and System Sciences
A simple three-dimensional real-time reliable cellular array
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
Neural and automata networks: dynamical behavior and applications
Neural and automata networks: dynamical behavior and applications
Neural networks: a systematic introduction
Neural networks: a systematic introduction
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Convergence of the Iterated Prisoner's Dilemma Game
Combinatorics, Probability and Computing
Large deviations for mean field models of probabilistic cellular automata
Random Structures & Algorithms
Fully asynchronous behavior of double-quiescent elementary cellular automata
Theoretical Computer Science
Slow emergence of cooperation for win-stay lose-shift on trees
Machine Learning
Directed Percolation Arising in Stochastic Cellular Automata Analysis
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Combined Effect of Topology and Synchronism Perturbation on Cellular Automata: Preliminary Results
ACRI '08 Proceedings of the 8th international conference on Cellular Automata for Reseach and Industry
Progresses in the analysis of stochastic 2D cellular automata: A study of asynchronous 2D minority
Theoretical Computer Science
Asynchronous behavior of double-quiescent elementary cellular automata
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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Cellular automata have been mainly studied on very regular graphs carrying the vertices (like lines or grids) and under synchronous dynamics (all vertices update simultaneously). In this paper, we study how the asynchronism and the graph act upon the dynamics of the classical minority rule. Minority has been well-studied for synchronous updates and is thus a reasonable choice to begin with. Yet, beyond its apparent simplicity, this rule yields complex behaviors when asynchronism is introduced. We investigate the transitory part as well as the asymptotic behavior of the dynamics under full asynchronism (also called sequential: only one random vertex updates at each time step) for several types of graphs. Such a comparative study is a first step in understanding how the asynchronous dynamics is linked to the topology (the graph). Previous analyses on the grid Regnault et al. (2009, 2010) [1,2] have observed that minority seems to induce fast stabilization. We investigate here this property on arbitrary graphs using tools such as energy, particles and random walks. We show that the worst case convergence time is, in fact, strongly dependent on the topology. In particular, we observe that the case of trees is nontrivial.