On the Bernoulli Automorphism of Reversible Linear Cellular Automata
arXiv:1503.05999 · doi:10.1016/j.ins.2016.01.062
Abstract
This investigation studies the ergodic properties of reversible linear cellular automata over for . 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.