English

On the Bernoulli Automorphism of Reversible Linear Cellular Automata

Dynamical Systems 2016-03-08 v3

Abstract

This investigation studies the ergodic properties of reversible linear cellular automata over Zm\mathbb{Z}_m for mNm \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.

Keywords

Cite

@article{arxiv.1503.05999,
  title  = {On the Bernoulli Automorphism of Reversible Linear Cellular Automata},
  author = {Chih-Hung Chang and Huilan Chang},
  journal= {arXiv preprint arXiv:1503.05999},
  year   = {2016}
}