Fully asynchronous behavior of double-quiescent elementary cellular automata
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Progresses in the analysis of stochastic 2D cellular automata: A study of asynchronous 2D minority
Theoretical Computer Science
Some formal properties of asynchronous callular automata
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
Theoretical Computer Science
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III
Directed percolation phenomena in asynchronous elementary cellular automata
ACRI'06 Proceedings of the 7th international conference on Cellular Automata for Research and Industry
Asynchronous cellular automata and dynamical properties
Natural Computing: an international journal
A study on learning robustness using asynchronous 1D cellular automata rules
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
Natural Computing: an international journal
m-Asynchronous cellular automata: from fairness to quasi-fairness
Natural Computing: an international journal
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In this paper we propose a probabilistic analysis of the relaxation time 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), under α-asynchronous dynamics (i.e., each cell is updated at each time step independently with probability 0 α ≤ 1). This work generalizes previous work in [1], in the sense that we study here a continuous range of asynchronism that goes from full asynchronism to full synchronism. We characterize formally the sensitivity to asynchronism of the relaxation times for 52 of the 64 considered automata. Our work relies on the design of probabilistic tools that enable to predict the global behaviour by counting local configuration patterns. These tools may be of independent interest since they provide a convenient framework to deal exhaustively with the tedious case analysis inherent to this kind of study. The remaining 12 automata (only 5 after symmetries) appear to exhibit interesting complex phenomena (such as polynomial/exponential/infinite phase transitions).