Inferring the Limit Behavior of Some Elementary Cellular Automata

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dc.contributor.authorRuivo E.L.P.
dc.contributor.authorDe Oliveira P.P.B.
dc.date.accessioned2024-03-13T00:49:09Z
dc.date.available2024-03-13T00:49:09Z
dc.date.issued2017
dc.description.abstract© 2017 World Scientific Publishing Company.Cellular automata locally define dynamical systems, discrete in space, time and in the state variables, capable of displaying arbitrarily complex global emergent behavior. One core question in the study of cellular automata refers to their limit behavior, that is, to the global dynamical features in an infinite time evolution. Previous works have shown that for finite time evolutions, the dynamics of one-dimensional cellular automata can be described by regular languages and, therefore, by finite automata. Such studies have shown the existence of growth patterns in the evolution of such finite automata for some elementary cellular automata rules and also inferred the limit behavior of such rules based upon the growth patterns; however, the results on the limit behavior were obtained manually, by direct inspection of the structures that arise during the time evolution. Here we present the formalization of an automatic method to compute such structures. Based on this, the rules of the elementary cellular automata space were classified according to the existence of a growth pattern in their finite automata. Also, we present a method to infer the limit graph of some elementary cellular automata rules, derived from the analysis of the regular expressions that describe their behavior in finite time. Finally, we analyze some attractors of two rules for which we could not compute the whole limit set.
dc.description.issuenumber8
dc.description.volume27
dc.identifier.doi10.1142/S0218127417300282
dc.identifier.issn0218-1274
dc.identifier.urihttps://dspace.mackenzie.br/handle/10899/35746
dc.relation.ispartofInternational Journal of Bifurcation and Chaos
dc.rightsAcesso Restrito
dc.subject.otherlanguageattractor
dc.subject.otherlanguagecomplexity
dc.subject.otherlanguageElementary cellular automata
dc.subject.otherlanguagefactorial language
dc.subject.otherlanguagelimit behavior
dc.subject.otherlanguageprocess graphs
dc.subject.otherlanguageregular language
dc.titleInferring the Limit Behavior of Some Elementary Cellular Automata
dc.typeArtigo
local.scopus.citations0
local.scopus.eid2-s2.0-85027191533
local.scopus.subjectattractor
local.scopus.subjectcomplexity
local.scopus.subjectElementary cellular automaton
local.scopus.subjectFactorial languages
local.scopus.subjectLimit behavior
local.scopus.subjectProcess graphs
local.scopus.updated2024-05-01
local.scopus.urlhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85027191533&origin=inward
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