On density determination with cellular automata: Results, constructions and directions

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dc.contributor.authorde Oliveira P.P.B.
dc.date.accessioned2024-03-13T01:01:29Z
dc.date.available2024-03-13T01:01:29Z
dc.date.issued2014
dc.description.abstract© 2014 Old City Publishing, Inc.The attempt to determine which is the most frequent cell state in an arbitrary initial configuration of a cellular automaton is quite likely the most well-studied benchmark problem in the context of computational ability of cellular automata. In its standard form, the problem is formulated in terms of a binary cellular automaton, whose action on a finite, one-dimensional lattice, with arbitrary odd-sized length and periodic boundary, would converge to a quiescent configuration of 1s or 0s, according to the respective prevailing bit in the initial configuration. Although extremely simple in formulation, the problem has unveiled a rich web of conceptual connections, which, at the same time, have enlarged and challenged our understanding about how to perform computations within cellular automata. In spite of the fact that the problem as such is knowingly impossible to solve, many proposals have been made in attempting to solve it, perfectly or not, in a variety of forms and generalisations. Here, we summarise the negative results in the context, and survey the main proposals with larger dimensions; higher number of states; fixed boundary conditions; infinite size lattices; asynchronous update schemes; rule changing throughout the temporal evolution; non-uniform cellular automata; memory addition to the rules; and stochastic rules. We also discuss burdens that would need to be overcome in the attempt to characterise the best possible imperfect solution in the standard formulation. The resulting picture clarifies what is known so far about the problem, and what is left to further investigation.
dc.description.firstpage357
dc.description.issuenumber5-6
dc.description.lastpage385
dc.description.volume9
dc.identifier.issn1557-5977
dc.identifier.urihttps://dspace.mackenzie.br/handle/10899/36438
dc.relation.ispartofJournal of Cellular Automata
dc.rightsAcesso Restrito
dc.subject.otherlanguageCellular automata
dc.subject.otherlanguageConservative rule
dc.subject.otherlanguageDCT
dc.subject.otherlanguageDensity classification task
dc.subject.otherlanguageEmergent computation
dc.subject.otherlanguageMajority problem
dc.titleOn density determination with cellular automata: Results, constructions and directions
dc.typeArtigo
local.scopus.citations32
local.scopus.eid2-s2.0-84921839804
local.scopus.subjectBinary cellular automata
local.scopus.subjectConservative rule
local.scopus.subjectDensity classification task
local.scopus.subjectEmergent computation
local.scopus.subjectFixed boundary conditions
local.scopus.subjectMajority problem
local.scopus.subjectNon-uniform cellular automaton
local.scopus.subjectOne-dimensional lattice
local.scopus.updated2024-05-01
local.scopus.urlhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84921839804&origin=inward
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