Neural and automata networks: dynamical behavior and applications
Neural and automata networks: dynamical behavior and applications
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Fully asynchronous behavior of double-quiescent elementary cellular automata
Theoretical Computer Science
Asynchronous behavior of double-quiescent elementary cellular automata
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Directed Percolation Arising in Stochastic Cellular Automata Analysis
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Examples of Fast and Slow Convergence of 2D Asynchronous Cellular Systems
ACRI '08 Proceedings of the 8th international conference on Cellular Automata for Reseach and Industry
Quick Energy Drop in Stochastic 2D Minority
ACRI '08 Proceedings of the 8th international conference on Cellular Automata for Reseach and Industry
On the Analysis of "Simple" 2D Stochastic Cellular Automata
Language and Automata Theory and Applications
Structural Sensitivity of Neural and Genetic Networks
MICAI '08 Proceedings of the 7th Mexican International Conference on Artificial Intelligence: Advances in Artificial Intelligence
Progresses in the analysis of stochastic 2D cellular automata: A study of asynchronous 2D minority
Theoretical Computer Science
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
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Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under asynchronous updates. Still, the few mathematical analyses of asynchronism focus on one-dimensional probabilistic cellular automata, either on single examples or on specific classes. As for other classic dynamical systems in physics, extending known methods from one- to two-dimensional systems is a long lasting challenging problem. In this paper, we address the problem of analysing an apparently simple 2D asynchronous cellular automaton: 2D Minority where each cell, when fired, updates to the minority state of its neighborhood. Our experiments reveal that in spite of its simplicity, the minority rule exhibits a quite complex response to asynchronism. By focusing on the fully asynchronous regime, we are however able to describe completely the asymptotic behavior of this dynamics as long as the initial configuration satisfies some natural constraints. Besides these technical results, we have strong reasons to believe that our techniques relying on defining an energy function from the transition table of the automaton may be extended to the wider class of threshold automata.