On the Bernoulli automorphism of reversible linear cellular automata

Chih-Hung Chang, Huilan Chang
2016 Information Sciences  
This investigation studies the ergodic properties of reversible linear cellular automata over Z_m for m ∈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.
doi:10.1016/j.ins.2016.01.062 fatcat:i23c4afwhbcjneptbrgdpgf3lu