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
A brief history of cellular automata
ACM Computing Surveys (CSUR)
The Intrinsic Universality Problem of One-Dimensional Cellular Automata
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Large deviations for mean field models of probabilistic cellular automata
Random Structures & Algorithms
Fully asynchronous behavior of double-quiescent elementary cellular automata
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Directed percolation phenomena in asynchronous elementary cellular automata
ACRI'06 Proceedings of the 7th international conference on Cellular Automata for Research and Industry
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
Theoretical Computer Science
Probing robustness of cellular automata through variations of asynchronous updating
Natural Computing: an international journal
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Cellular automata are both seen as a model of computation and as tools to model real life systems. Historically they were studied under synchronous dynamics where all the cells of the system are updated at each time step. Meanwhile the question of probabilistic dynamics emerges: on the one hand, to develop cellular automata which are capable of reliable computation even when some random errors occur [24,14,13]; on the other hand, because synchronous dynamics is not a reasonable assumption to simulate real life systems.Among cellular automata a specific class was largely studied in synchronous dynamics : the elementary cellular automata (ECA). These are the "simplest" cellular automata. Nevertheless they exhibit complex behaviors and even Turing universality. Several studies [20,7,8,5] have focused on this class under 茂戮驴-asynchronous dynamics where each cell has a probability 茂戮驴to be updated independently. It has been shown that some of these cellular automata exhibit interesting behavior such as phase transition when the asynchronicity rate 茂戮驴varies.Due to their richness of behavior, probabilistic cellular automata are also very hard to study. Almost nothing is known of their behavior [20]. Understanding these "simple" rules is a key step to analyze more complex systems. We present here a coupling between oriented percolation and ECA 178 and confirms observations made in [5] that percolation may arise in cellular automata. As a consequence this coupling shows that there is a positive probability that the ECA 178 does not reach a stable configuration as soon as the initial configuration is not a stable configuration and 茂戮驴 0.996. Experimentally, this result seems to stay true as soon as 茂戮驴 茂戮驴c≈ 0.5.