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
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
On the Analysis of "Simple" 2D Stochastic Cellular Automata
Language and Automata Theory and Applications
Progresses in the analysis of stochastic 2D cellular automata: A study of asynchronous 2D minority
Theoretical Computer Science
Brothers in Arms? On AI Planning and Cellular Automata
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Some formal properties of asynchronous callular automata
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
Theoretical Computer Science
Asynchronous cellular automata and dynamical properties
Natural Computing: an international journal
Progresses in the analysis of stochastic 2D cellular automata: a study of asynchronous 2D minority
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Computation of functions on n bits by asynchronous clocking of cellular automata
Natural Computing: an international journal
m-Asynchronous cellular automata: from fairness to quasi-fairness
Natural Computing: an international journal
Computing Issues of Asynchronous CA
Fundamenta Informaticae
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In this paper we propose a probabilistic analysis of the fully asynchronous behavior (i.e., two cells are never simultaneously updated, as in a continuous time process) of elementary finite cellular automata (i.e., {0, 1} states, radius 1 and unidimensional) for which both states are quiescent (i.e., (0, 0, 0) ↦ 0 and (1, 1, 1) ↦ 1). It has been experimentally shown in previous works that introducing asynchronism in the global function of a cellular automata was perturbing its behavior, but as far as we know, only few theoretical work exists on the subject. The cellular automata we consider live on a ring of size n and asynchronism is introduced as follows: at each time step one cell is selected uniformly at random and the transition is made on this cell while the others stay in the same state. Among the 64 cellular automata belonging to the class we consider, we show that 9 of them diverge on all non-trivial configurations while the 55 other converge almost surely to a random fixed point. We show that the exact convergence time of these 55 automata can only take the following values: either 0, Θ(n ln n), Θ(n2), Θ(n3 ) or Θ(n2n). Furthermore, the global behavior of each of these cellular automata is fully determined by reading its code.