An asynchronous solution to the synchronisation problem for binary one-dimensional cellular automata

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dc.contributor.authorRuivo E.L.P.
dc.contributor.authorBalbi P.P.
dc.contributor.authorPerrot K.
dc.date.accessioned2024-03-12T23:45:56Z
dc.date.available2024-03-12T23:45:56Z
dc.date.issued2020
dc.description.abstract© 2020 Elsevier B.V.Because cellular automata rely on totally local and synchronous processing at the neighbourhood of each cell, the issue of global synchronisation of the cell states has a long tradition in cellular automata literature. Here, the following benchmark synchronisation problem in the context of one-dimensional binary cellular automata rule is addressed: in periodic boundary condition, a rule needs to be conceived so as to lead any initial configuration to converge, at some time in future, to a cyclic regime of period 2 characterised by all cells alternating between fully homogeneous configurations of 0s and 1s. In spite of its simplicity, the problem has recently been shown not to have a solution by synchronously updating the cell states. In contrast, we provide a perfect solution to the problem, with a 4-neighbour rule, by replacing the synchronous update of the cells of the lattice with a deterministic, block sequential asynchronous update schedule. Achieving synchrony by asynchronous means represents an example that makes it evident the fact that asynchrony can be explored to give more freedom to the cells of a CA, in terms of the local information they exchange with each other. Since synchronisation phenomena and problems are pervasive in many contexts in science and engineering, it is a valuable resource to understand how synchronisation can be achieved and controlled in simple computational models, such as cellular automata.
dc.description.volume413
dc.identifier.doi10.1016/j.physd.2020.132554
dc.identifier.issn0167-2789
dc.identifier.urihttps://dspace.mackenzie.br/handle/10899/34866
dc.relation.ispartofPhysica D: Nonlinear Phenomena
dc.rightsAcesso Restrito
dc.subject.otherlanguageAsynchrony
dc.subject.otherlanguageBlock sequential asynchronous update
dc.subject.otherlanguageCellular automata
dc.subject.otherlanguageDeterministic update schedules
dc.subject.otherlanguageSynchronisation problem
dc.subject.otherlanguageSynchronism
dc.titleAn asynchronous solution to the synchronisation problem for binary one-dimensional cellular automata
dc.typeArtigo
local.scopus.citations4
local.scopus.eid2-s2.0-85089032210
local.scopus.subjectAsynchronous update
local.scopus.subjectBinary cellular automata
local.scopus.subjectBlock-sequential
local.scopus.subjectComputational model
local.scopus.subjectInitial configuration
local.scopus.subjectLocal information
local.scopus.subjectPeriodic boundary conditions
local.scopus.subjectScience and engineering
local.scopus.updated2024-05-01
local.scopus.urlhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85089032210&origin=inward
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