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Author Leal, L.; Montealegre, P.; Osses, A.; Rapaport, I.
Title (up) A large diffusion and small amplification dynamics for density classification on graphs Type
Year 2022 Publication International Journal Of Modern Physics C Abbreviated Journal Int. J. Mod Phys. C
Volume Early Access Issue Pages
Keywords Automata networks; density classification; Laplacian matrix
Abstract The density classification problem on graphs consists in finding a local dynamics such that, given a graph and an initial configuration of 0's and 1's assigned to the nodes of the graph, the dynamics converge to the fixed point configuration of all 1's if the fraction of 1's is greater than the critical density (typically 1/2) and, otherwise, it converges to the all 0's fixed point configuration. To solve this problem, we follow the idea proposed in [R. Briceno, P. M. de Espanes, A. Osses and I. Rapaport, Physica D 261, 70 (2013)], where the authors designed a cellular automaton inspired by two mechanisms: diffusion and amplification. We apply this approach to different well-known graph classes: complete, regular, star, Erdos-Renyi and Barabasi-Albert graphs.
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 0129-1831 ISBN Medium
Area Expedition Conference
Notes WOS:000882906900002 Approved
Call Number UAI @ alexi.delcanto @ Serial 1656
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Author Lobos, F.; Goles, E.; Ruivo, E.L.P.; de Oliveira, P.P.B.; Montealegre, P.
Title (up) 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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