On the Bernoulli automorphism of reversible linear cellular automata

This investigation studies the ergodic properties of reversible linear cellular automata over Zm 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 by Pivato [20] for the case of...

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Bibliographic Details
Published in:Information sciences 2016-06, Vol.345, p.217-225
Main Authors: Chang, Chih-Hung, Chang, Huilan
Format: Article
Language:English
Subjects:
Automorphisms
Bernoulli automorphism
Cellular automata
Ergodic processes
Invertible cellular automata
Measure-preserving transformation
Strong mixing
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Summary:This investigation studies the ergodic properties of reversible linear cellular automata over Zm 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 by Pivato [20] for the case of reversible linear cellular automata.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2016.01.062