On the complexity of two-dimensional signed majority cellular automata

Abstract : We study the complexity of signed majority cellular automata on the planar grid. We show that, depending on their symmetry and uniformity, they can simulate different types of logical circuitry under different modes. We use this to establish new bounds on their overall complexity, concretely: the uniform asymmetric and the non-uniform symmetric rules are Turing universal and have a P-complete prediction problem; the non-uniform asymmetric rule is in-trinsically universal; no symmetric rule can be intrinsically universal. We also show that the uniform asymmetric rules exhibit cycles of super-polynomial length, whereas symmetric ones are known to have bounded cycle length.
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https://hal.archives-ouvertes.fr/hal-01472161
Contributeur : Guillaume Theyssier <>
Soumis le : lundi 20 février 2017 - 15:43:27
Dernière modification le : vendredi 26 octobre 2018 - 10:34:30
Document(s) archivé(s) le : dimanche 21 mai 2017 - 14:43:26

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GMPT-thresholdDyn-JCSS.pdf
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Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales 4.0 International License

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  • HAL Id : hal-01472161, version 1

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Eric Goles, Pedro Montealegre, Kévin Perrot, Guillaume Theyssier. On the complexity of two-dimensional signed majority cellular automata. 2017. 〈hal-01472161〉

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