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Author Goles, E.; Moreira, A.
Title Number-Conserving Cellular Automata and Communication Complexity: A Numerical Exploration Beyond Elementary CAs Type
Year 2012 Publication Journal Of Cellular Automata Abbreviated Journal J. Cell. Autom.
Volume 7 Issue 2 Pages 151-165
Keywords Number-Conserving; Communication Complexity; One-dimensional Cellular Automata
Abstract We perform a numerical exploration of number-conserving cellular automata (NCCA) beyond the class of elementary CAs, in search of examples with high communication complexity. We consider some possible generalizations of the elementary rule 184 (a minimal model of traffic, which is the only non-trivial elementary NCCA). as well as the classes of NCCAs which minimally extend either the radius or the state set (with respect to the 2 states and radius 1 of the elementary case). Both for 3 states and radius 1, and for 2 stales and radius 2, NCCA appear that are conjectured to have maximal (exponential) communication complexity. Examples are given also for (conjectured) linear and quadratic behaviour.
Address [Goles, Eric] Univ Adolfo Ibanez, Santiago, Chile, Email: andres.moreira@usm.cl
Corporate Author Thesis
Publisher Old City Publishing Inc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1557-5969 ISBN Medium
Area Expedition Conference
Notes WOS:000302978700004 Approved
Call Number UAI @ eduardo.moreno @ Serial 210
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Author Goles, E.; Lobos, F.; Montealegre, P.; Ruivo, ELP.; de Oliveira, PPB.
Title Computational Complexity of the Stability Problem for Elementary Cellular Automata Type
Year 2020 Publication Journal of Cellular Automata Abbreviated Journal J. Cell. Autom.
Volume 15 Issue 4 Pages 261-304
Keywords One-dimensional cellular automata; elementary cellular automata; computational complexity; stability problem; decision problem
Abstract Given an elementary cellular automaton and a cell v, we define the stability decision problem as the determination of whether or not the state of cell v will ever change, at least once, during the time evolution of the rule, over a finite input configuration. Here, we perform the study of the entire elementary cellular automata rule space, for the two possible decision cases of the problem, namely, changes in v from state 0 to 1 (0 -> 1), and the other way round (1 -> 0). Out of the 256 elementary cellular automata, we show that for all of them, at least one of the two decision problems is in the NC complexity class.
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 1557-5969 ISBN Medium
Area Expedition Conference
Notes WOS:000613086900002 Approved
Call Number UAI @ alexi.delcanto @ Serial 1329
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Author Goles, E.; Montalva-Medel, M.; MacLean, S.; Mortveit, H.
Title Block Invariance in a Family of Elementary Cellular Automata Type
Year 2018 Publication Journal Of Cellular Automata Abbreviated Journal J. Cell. Autom.
Volume 13 Issue 1-2 Pages 15-32
Keywords Elementary cellular automata; block updates; periodic configurations; block invariance
Abstract We study the steady state invariance of elementary cellular automata (ECA) under different deterministic updating schemes. Specifically, we study a family of eleven ECA whose steady state invariance were left under conjecture in [2].
Address [Goles, Eric; Montalva-Medel, Marco; MacLean, Stephanie] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: eric.chacc@uai.cl;
Corporate Author Thesis
Publisher Old City Publishing Inc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1557-5969 ISBN Medium
Area Expedition Conference
Notes WOS:000410888100002 Approved
Call Number UAI @ eduardo.moreno @ Serial 782
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Author Goles, E.; Montalva-Medel, M.; Mortveit, H.; Ramirez-Flandes, S.
Title Block Invariance in Elementary Cellular Automata Type
Year 2015 Publication Journal Of Cellular Automata Abbreviated Journal J. Cell. Autom.
Volume 10 Issue 1-2 Pages 119-135
Keywords Elementary cellular automata; block updates; periodic points; block invariance
Abstract Consider an elementary cellular automaton (ECA) under periodic boundary conditions. Given an arbitrary partition of the set of vertices we consider the block updating, i.e. the automaton's local function is applied from the first to the last set of the partition such that vertices belonging to the same set are updated synchronously. The automaton is said block-invariant if the set of periodic configurations is independent of the choice of the block updating. When the sets of the partition are singletons we have the sequential updating: vertices are updated one by one following a permutation pi. In [5] the authors analyzed the pi-invariance of the 2(8) = 256 possible ECA rules (or the 88 non-redundant rules subset). Their main result was that for all n > 3, exactly 41 of these non-redundant rules are pi-invariant. In this paper we determine the subset of these 41 rules that are block invariant. More precisely, for all n > 3, exactly 15 of these rules are block invariant. Moreover, we deduce that block invariance also implies that the attractor structure itself is independent of the choice of the block update.
Address [Goles, Eric; Montalva-Medel, Marco; Ramirez-Flandes, Salvador] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Penalolen, Chile, Email: eric.chacc@uai.cl;
Corporate Author Thesis
Publisher Old City Publishing Inc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1557-5969 ISBN Medium
Area Expedition Conference
Notes WOS:000350183000006 Approved
Call Number UAI @ eduardo.moreno @ Serial 461
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Author Goles, E.; Montealegre, P.; Vera, J.
Title Naming Game Automata Networks Type
Year 2016 Publication Journal Of Cellular Automata Abbreviated Journal J. Cell. Autom.
Volume 11 Issue 5-6 Pages 497-521
Keywords Automata networks; cellular automata; majority functions; energy operator; naming game; fixed points; limit cycles
Abstract In this paper we introduce automata networks to model some features of the emergence of a vocabulary related with the naming game model. We study the dynamical behaviour (attractors and convergence) of extremal and majority local functions.
Address [Goles, Eric; Vera, Javier] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Avda Diagonal Las Torres 2640, Santiago, Chile, Email: eric.chacc@uai.cl;
Corporate Author Thesis
Publisher Old City Publishing Inc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1557-5969 ISBN Medium
Area Expedition Conference
Notes WOS:000382426500007 Approved
Call Number UAI @ eduardo.moreno @ Serial 649
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Author Lobos, F.; Goles, E.; Ruivo, E.L.P.; de Oliveira, P.P.B.; Montealegre, P.
Title Mining a Class of Decision Problems for One-dimensional Cellular Automata Type
Year 2018 Publication Journal Of Cellular Automata Abbreviated Journal J. Cell. Autom.
Volume 13 Issue 5-6 Pages 393-405
Keywords One-dimensional cellular automata; decision problems; density classification; parity problem
Abstract Cellular automata are locally defined, homogeneous dynamical systems, discrete in space, time and state variables. Within the context of one-dimensional, binary, cellular automata operating on cyclic configurations of odd length, we consider the general decision problem: if the initial configuration satisfies a given property, the lattice should converge to the fixed-point of all 1s ((1) over right arrow), or to (0) over right arrow, otherwise. Two problems in this category have been widely studied in the literature, the parity problem [1] and the density classification task [4]. We are interested in determining all cellular automata rules with neighborhood sizes of 2, 3, 4 and 5 cells (i.e., radius r of 0.5, 1, 1.5 and 2.5) that solve decision problems of the previous type. We have demonstrated a theorem that, for any given rule in those spaces, ensures the non existence of fixed points other than (0) over right arrow and (1) over right arrow for configurations of size larger than 2(2r), provided that the rule does not support different fixed points for any configuration with size smaller than or equal to 2(2r). In addition, we have a proposition that ensures the convergence to only (0) over right arrow or (1) over right arrow of any initial configuration, if the rule complies with given conditions. By means of theoretical and computational approaches, we determined that: for the rule spaces defined by radius 0.5 and r = 1, only 1 and 2 rules, respectively, converge to (1) over right arrow or (0) over right arrow, to any initial configuration, and both recognize the same language, and for the rule space defined by radius r = 1.5, 40 rules satisfy this condition and recognize 4 different languages. Finally, for the radius 2 space, out of the 4,294,967,296 different rules, we were able to significantly filter it out, down to 40,941 candidate rules. We hope such an extensive mining should unveil new decision problems of the type widely studied in the literature.
Address [Lobos, Fabiola; Goles, Eric; Montealegre, Pedro] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Ave Diagonal Torres 2640, Santiago, Chile, Email: pp.balbi@gmail.com
Corporate Author Thesis
Publisher Old City Publishing Inc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1557-5969 ISBN Medium
Area Expedition Conference
Notes WOS:000449762900002 Approved
Call Number UAI @ eduardo.moreno @ Serial 931
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