Reversibility of number-conserving 1D cellular automata: Unlocking insights into the dynamics for larger state sets

Discrete dynamical systems such as cellular automata are vastly used as models of complex physical phenomena. For this reason, the problem of reversibility of such systems is very important and recurrently taken up by researchers. Unfortunately, the study of reversibility is remarkably hard, even in...

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Bibliographic Details
Published in:Physica. D 2022-01, Vol.429, p.133075, Article 133075
Main Authors: Wolnik, Barbara, Dziemiańczuk, Maciej, Dzedzej, Adam, De Baets, Bernard
Format: Article
Language:English
Subjects:
Cellular automata
Number conservation
Reversibility
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Summary:Discrete dynamical systems such as cellular automata are vastly used as models of complex physical phenomena. For this reason, the problem of reversibility of such systems is very important and recurrently taken up by researchers. Unfortunately, the study of reversibility is remarkably hard, even in the case of one-dimensional cellular automata. We propose a novel method that really supports the investigation of the reversibility of number-conserving cellular automata, i.e, cellular automata that preserve the sum of the states of all the cells upon every update. This method allows to enumerate all so-called k-ary (binary, ternary, quaternary, quinary, etc.) number-conserving cellular automata that are reversible and this for a fairly wide range of values of the parameter k. •Algorithms for enumeration of 1D reversible number-conserving cellular automata.•Use cases for 1D reversible number-conserving CA with five, six, and seven states.•Comprehensive description of dynamics for such CA with five states is presented.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2021.133075