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Author (up) Goles, E.; Montealegre, P.; Perrot, K.
Title Freezing sandpiles and Boolean threshold networks: Equivalence and complexity Type
Year 2021 Publication Advances In Applied Mathematics Abbreviated Journal Adv. Appl. Math.
Volume 125 Issue Pages 102161
Keywords
Abstract The NC versus P-hard classification of the prediction problem for sandpiles on the two dimensional grid with von Neumann neighborhood is a famous open problem. In this paper we make two kinds of progresses, by studying its freezing variant. First, it enables to establish strong connections with other well known prediction problems on networks of threshold Boolean functions such as majority. Second, we can highlight some necessary and sufficient elements to the dynamical complexity of sandpiles, with a surprisingly crucial role of cells with two grains. (C) 2021 Elsevier Inc. All rights reserved.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0196-8858 ISBN Medium
Area Expedition Conference
Notes WOS:000614706400006 Approved
Call Number UAI @ alexi.delcanto @ Serial 1340
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Author (up) 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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Author (up) Perrot, K.; Montalva-Medel, M.; de Oliveira, P.P.B.; Ruivo, E.L.P.
Title Maximum sensitivity to update schedules of elementary cellular automata over periodic configurations Type
Year 2020 Publication Natural Computing Abbreviated Journal Nat. Comput.
Volume 19 Issue 1 Pages 51-90
Keywords Synchronism sensitivity; Elementary cellular automata; Update digraph
Abstract This work is a thoughtful extension of the ideas sketched in Montalva et al. (AUTOMATA 2017 exploratory papers proceedings, 2017), aiming at classifying elementary cellular automata (ECA) according to their maximal one-step sensitivity to changes in the schedule of cells update. It provides a complete classification of the ECA rule space for all period sizes n[ 9 and, together with the classification for all period sizes n <= 9 presented in Montalva et al. (Chaos Solitons Fractals 113:209-220, 2018), closes this problem and opens further questionings. Most of the 256 ECA rule's sensitivity is proved or disproved to be maximum thanks to an automatic application of basic methods. We formalize meticulous case disjunctions that lead to the results, and patch failing cases for some rules with simple arguments. This gives new insights on the dynamics of ECA rules depending on the proof method employed, as for the last rules 45 and 105 requiring o0011THORN induction patterns.
Address [Perrot, Kevin] Univ, Aix Marseille Univ.,Toulon,CNRS,UMR 7020, Marseille, France, Email: kevin.perrot@lis-lab.fr
Corporate Author Thesis
Publisher Springer Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1567-7818 ISBN Medium
Area Expedition Conference
Notes WOS:000517129300006 Approved
Call Number UAI @ eduardo.moreno @ Serial 1162
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Author (up) Ruivo, E.L.P.; de Oliveira, P.P.B.; Montalva-Medel, M.; Perrot, K.
Title Maximum sensitivity to update schedules of elementary cellular automata over infinite configurations Type
Year 2020 Publication Information and Computation Abbreviated Journal Inf. Comput.
Volume 274 Issue SI Pages 104538
Keywords
Abstract Cellular automata are discrete dynamical systems with locally defined behaviour, well known as simple models of complex systems. Classically, their dynamics derive from synchronously iterated rules over finite or infinite configurations; however, since for many natural systems to be modelled, asynchrony seems more plausible, asynchronous iteration of the rules has gained a considerable attention in recent years. One question in this context is how changing the update schedule of rule applications affects the global behaviour of the system. In particular, previous works addressed the notion of maximum sensitivity to changes in the update schemes for finite lattices. Here, we extend the notion to infinite lattices, and classify elementary cellular automata space according to such a property.
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Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0890-5401 ISBN Medium
Area Expedition Conference
Notes Approved
Call Number UAI @ eduardo.moreno @ Serial 1122
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Author (up) Ruivo, E.L.P.; Montalva-Medel, M.; de Oliveira, P.P.B.; Perrot, K.
Title Characterisation of the elementary cellular automata in terms of their maximum sensitivity to all possible asynchronous updates Type
Year 2018 Publication Chaos Solitons & Fractals Abbreviated Journal Chaos Solitons Fractals
Volume 113 Issue Pages 209-220
Keywords Cellular automaton; Asynchronous update; Update digraph; Discrete dynamics; One-step maximum sensitivity
Abstract Cellular automata are fully-discrete dynamical systems with global behaviour depending upon their locally specified state transitions. They have been extensively studied as models of complex systems as well as objects of mathematical and computational interest. Classically, the local rule of a cellular automaton is iterated synchronously over the entire configuration. However, the question of how asynchronous updates change the behaviour of a cellular automaton has become a major issue in recent years. Here, we analyse the elementary cellular automata rule space in terms of how many different one-step trajectories a rule would entail when taking into account all possible deterministic ways of updating the rule, for one time step, over all possible initial configurations. More precisely, we provide a characterisation of the elementary cellular automata, by means of their one-step maximum sensitivity to all possible update schedules, that is, the property that any change in the update schedule causes the rule's one-step trajectories also to change after one iteration. Although the one-step maximum sensitivity does not imply that the remainder of the time-evolutions will be distinct, it is a necessary condition for that. (C) 2018 Elsevier Ltd. All rights reserved.
Address [Ruivo, Eurico L. P.; de Oliveira, Pedro P. B.] Univ Presbiteriana Mackenzie, Fac Comp & Informat, Sao Paulo, SP, Brazil, Email: eurico.ruivo@mackenzie.br
Corporate Author Thesis
Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0960-0779 ISBN Medium
Area Expedition Conference
Notes WOS:000442101600024 Approved
Call Number UAI @ eduardo.moreno @ Serial 910
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