Reliable computation with cellular automata
Journal of Computer and System Sciences
Neural and automata networks: dynamical behavior and applications
Neural and automata networks: dynamical behavior and applications
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
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
Hi-index | 0.00 |
Cellular automata are usually updated synchronously and thus deterministically. The question of stochastic dynamics arises in the development of cellular automata resistant to noise [1] and in simulation of real life systems [2]. Synchronous updates may not be a valid hypothesis for such simulations and most of these studies use stochastic versions of cellular automata.In [3,4,5,6], the authors study different classes of cellular automata under fully asynchronous dynamics (only one random cell fires at each time step) and 茂戮驴-asynchronous dynamics (each cell has a probability 茂戮驴to fire at each time step). They develop tools and methods to ease the study of other cellular automata. In [4,6], they analyze 2D Minority under fully asynchronous dynamics for Von Neumann and Moore neighborhoods. The behavior of this cellular automaton under these dynamics is surprisingly rich. The energy of a configuration is an useful information. In [4], it is proved that configurations of energy greater than $\frac{5mn}{3}$ (where mand nare the length and the width of the configuration) will not appear in the long range behavior of 2D minority for Von Neumann neighborhood. In this paper we improve this bound to $18\lceil \frac{m}{4} \rceil \lceil \frac{n}{4} \rceil$. The proof is based on an enumeration of cases made by computer. This method could be easily tuned for other cellular automata or neighborhoods.