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Author Goles, E.; Meunier, P.E.; Rapaport, I.; Theyssier, G.
Title Communication complexity and intrinsic universality in cellular automata Type
Year 2011 Publication Theoretical Computer Science Abbreviated Journal Theor. Comput. Sci.
Volume 412 Issue 1-2 Pages 2-21
Keywords Cellular automata; Communication complexity; Intrinsic universality
Abstract The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most cases. In this article, we introduce necessary conditions for a cellular automaton to be “universal”, according to a precise notion of simulation, related both to the dynamics of cellular automata and to their computational power. This notion of simulation relies on simple operations of space-time rescaling and it is intrinsic to the model of cellular automata. intrinsic universality, the derived notion, is stronger than Turing universality, but more uniform, and easier to define and study. Our approach builds upon the notion of communication complexity, which was primarily designed to study parallel programs, and thus is, as we show in this article, particulary well suited to the study of cellular automata: it allowed us to show, by studying natural problems on the dynamics of cellular automata, that several classes of cellular automata, as well as many natural (elementary) examples, were not intrinsically universal. (C) 2010 Elsevier B.V. All rights reserved.
Address [Meunier, P. -E.; Theyssier, G.] Univ Savoie, CNRS, LAMA, F-73376 Le Bourget Du Lac, France, Email: guillaume.theyssier@univ-savoie.fr
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0304-3975 ISBN Medium
Area Expedition Conference
Notes WOS:000285952400002 Approved
Call Number UAI @ eduardo.moreno @ Serial 118
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Author Goles, E.; Montealegre, P.; Perrot, K.; Theyssier, G.
Title On the complexity of two-dimensional signed majority cellular automata Type
Year 2018 Publication Journal Of Computer And System Sciences Abbreviated Journal J. Comput. Syst. Sci.
Volume 91 Issue Pages 1-32
Keywords Cellular automata dynamics; Majority cellular automata; Signed two-dimensional lattice; Turing universal; Intrinsic universal; Computational complexity
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 intrinsically 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. (C) 2017 Elsevier Inc. All rights reserved.
Address [Goles, Eric; Montealegre, Pedro] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: p.montealegre@uai.cl
Corporate Author Thesis
Publisher Academic Press Inc Elsevier Science Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0022-0000 ISBN Medium
Area Expedition Conference
Notes WOS:000413130200001 Approved
Call Number UAI @ eduardo.moreno @ Serial 779
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