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On the decomposition of stochastic cellular automata
In this paper we present two interesting properties of stochastic cellular
automata that can be helpful in analyzing the dynamical behavior of such
automata. The first property allows for calculating cell-wise probability
distributions over the state set of a stochastic cellular automaton, i.e.
images that show the average state of each cell during the evolution of the
stochastic cellular automaton. The second property shows that stochastic
cellular automata are equivalent to so-called stochastic mixtures of
deterministic cellular automata. Based on this property, any stochastic
cellular automaton can be decomposed into a set of deterministic cellular
automata, each of which contributes to the behavior of the stochastic cellular
automaton.Comment: Submitted to Journal of Computation Science, Special Issue on
Cellular Automata Application