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arXiv · 1503.05999

On the Bernoulli Automorphism of Reversible Linear Cellular Automata

Chih-Hung Chang·Huilan Chang
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Abstract

This investigation studies the ergodic properties of reversible linear cellular automata over $\mathbb{Z}_m$ for $m \in \mathbb{N}$. We show that a reversible linear cellular automaton is either a Bernoulli automorphism or non-ergodic. This gives an affirmative answer to an open problem proposed in [Pivato, Ergodc theory of cellular automata, Encyclopedia of Complexity and Systems Science, 2009, pp.~2980-3015] for the case of reversible linear cellular automata.

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Chih-Hung Chang, Huilan Chang. 2015-03-20. On the Bernoulli Automorphism of Reversible Linear Cellular Automata. https://doi.org/10.1016/j.ins.2016.01.062

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