2,103 research outputs found
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
Sensitivity to noise and ergodicity of an assembly line of cellular automata that classifies density
We investigate the sensitivity of the composite cellular automaton of H.
Fuk\'{s} [Phys. Rev. E 55, R2081 (1997)] to noise and assess the density
classification performance of the resulting probabilistic cellular automaton
(PCA) numerically. We conclude that the composite PCA performs the density
classification task reliably only up to very small levels of noise. In
particular, it cannot outperform the noisy Gacs-Kurdyumov-Levin automaton, an
imperfect classifier, for any level of noise. While the original composite CA
is nonergodic, analyses of relaxation times indicate that its noisy version is
an ergodic automaton, with the relaxation times decaying algebraically over an
extended range of parameters with an exponent very close (possibly equal) to
the mean-field value.Comment: Typeset in REVTeX 4.1, 5 pages, 5 figures, 2 tables, 1 appendix.
Version v2 corresponds to the published version of the manuscrip
A Graph Theory Approach for Regional Controllability of Boolean Cellular Automata
Controllability is one of the central concepts of modern control theory that
allows a good understanding of a system's behaviour. It consists in
constraining a system to reach the desired state from an initial state within a
given time interval. When the desired objective affects only a sub-region of
the domain, the control is said to be regional. The purpose of this paper is to
study a particular case of regional control using cellular automata models
since they are spatially extended systems where spatial properties can be
easily defined thanks to their intrinsic locality. We investigate the case of
boundary controls on the target region using an original approach based on
graph theory. Necessary and sufficient conditions are given based on the
Hamiltonian Circuit and strongly connected component. The controls are obtained
using a preimage approach
Response Curves and Preimage Sequences of Two-Dimensional Cellular Automata
We consider the problem of finding response curves for a class of binary
two-dimensional cellular automata with -shaped neighbourhood. We show that
the dependence of the density of ones after an arbitrary number of iterations,
on the initial density of ones, can be calculated for a fairly large number of
rules by considering preimage sets. We provide several examples and a summary
of all known results. We consider a special case of initial density equal to
0.5 for other rules and compute explicitly the density of ones after
iterations of the rule. This analysis includes surjective rules, which in the
case of -shaped neighbourhood are all found to be permutive. We conclude
with the observation that all rules for which preimage curves can be computed
explicitly are either finite or asymptotic emulators of identity or shift.Comment: 7 pages, 3 figure
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