Minimal entropy approximation for cellular automata

We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with...

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Bibliographic Details
Published in:Journal of statistical mechanics 2014-02, Vol.2014 (2), p.P02009-20
Main Author: Fuk, Henryk
Format: Article
Language:English
Subjects:
Approximation
Cellular automata
Construction
Density
Entropy
Mathematical analysis
Orbits
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Summary:We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim.
ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/2014/02/P02009