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Natural Computing

Remarks on the cellular automaton global synchronisation problem: deterministic versus stochastic models

  • 12-05-2018
Published in:
Author
Nazim Fatès
Published in
Natural Computing | Issue 3/2019

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Abstract

In the global synchronisation problem, one is asked to find a cellular automaton which has the property that every initial condition evolves into a homogeneous blinking state. We study this simple inverse problem for the case of one-dimensional systems with periodic boundary conditions. Two paradoxical observations are made: (a) despite the apparent simplicity of finding rules with good statistical results, there exist no perfect deterministic solutions to this problem, (b) if we allow the use of randomness in the local rule, constructing “perfect” stochastic solutions is easy. For the stochastic case, we give some rules for which the mean time of synchronisation varies quadratically with the number of cells and ask if this result can be improved. To explore more deeply the deterministic rules, we code our problem as a SAT problem and use SAT solvers to find rules that synchronise a large set of initial conditions (in appendix).

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previous article A universal non-conservative reversible elementary triangular partitioned cellular automaton that shows complex behavior
next article Cellular automata and finite groups
Title
Remarks on the cellular automaton global synchronisation problem: deterministic versus stochastic models
Author
Nazim Fatès
Publication date
12-05-2018
Publisher
Springer Netherlands
Published in
Natural Computing / Issue 3/2019
Print ISSN: 1567-7818
Electronic ISSN: 1572-9796
DOI
https://doi.org/10.1007/s11047-018-9683-0
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