43,922 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
Descriptional complexity of cellular automata and decidability questions
We study the descriptional complexity of cellular automata (CA), a parallel model of computation. We show that between one of the simplest cellular models, the realtime-OCA. and "classical" models like deterministic finite automata (DFA) or pushdown automata (PDA), there will be savings concerning the size of description not bounded by any recursive function, a so-called nonrecursive trade-off. Furthermore, nonrecursive trade-offs are shown between some restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semi decidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata
Phase Space Invertible Asynchronous Cellular Automata
While for synchronous deterministic cellular automata there is an accepted
definition of reversibility, the situation is less clear for asynchronous
cellular automata. We first discuss a few possibilities and then investigate
what we call phase space invertible asynchronous cellular automata in more
detail. We will show that for each Turing machine there is such a cellular
automaton simulating it, and that it is decidable whether an asynchronous
cellular automaton has this property or not, even in higher dimensions.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
A compact topology for sand automata
In this paper, we exhibit a strong relation between the sand automata
configuration space and the cellular automata configuration space. This
relation induces a compact topology for sand automata, and a new context in
which sand automata are homeomorphic to cellular automata acting on a specific
subshift. We show that the existing topological results for sand automata,
including the Hedlund-like representation theorem, still hold. In this context,
we give a characterization of the cellular automata which are sand automata,
and study some dynamical behaviors such as equicontinuity. Furthermore, we deal
with the nilpotency. We show that the classical definition is not meaningful
for sand automata. Then, we introduce a suitable new notion of nilpotency for
sand automata. Finally, we prove that this simple dynamical behavior is
undecidable
Randomized Cellular Automata
We define and study a few properties of a class of random automata networks.
While regular finite one-dimensional cellular automata are defined on periodic
lattices, these automata networks, called randomized cellular automata, are
defined on random directed graphs with constant out-degrees and evolve
according to cellular automaton rules. For some families of rules, a few
typical a priori unexpected results are presented.Comment: 13 pages, 7 figure
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