Synchronous solution of the parity problem on cyclic configurations, with elementary cellular automaton rule 150, over a family of directed, non-circulant, regular graphs

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dc.contributor.authorBalbi P.P.
dc.contributor.authorRuivo E.
dc.contributor.authorFaria F.
dc.date.accessioned2024-03-12T19:13:33Z
dc.date.available2024-03-12T19:13:33Z
dc.date.issued2022
dc.description.abstract© 2022 Elsevier Inc.The parity problem is one of the classical benchmarks for probing the computational ability of cellular automata. It refers to conceiving a rule to allow deciding whether the number of 1s in an arbitrary binary sequence is an odd or even number, without resorting to globally accessing the sequence. In its most traditional formulation, it refers to cyclic configurations of odd length, which, under the action of a cellular automaton, should converge to a fixed point of all cells in the 0-state, if the configuration initially has an even number of 1s, or to a fixed point of all cells in the 1-state, otherwise. It has been shown that the problem can be solved in this formulation, in particular by a rule alone. Here, we provide a synchronous solution to the problem, by relying upon elementary cellular automaton rule 150, the elementary local parity rule, over a connection pattern among the cells defined by a family of directed, non-circulant, regular graphs. This represents the simplest synchronous solution currently known for cyclic configurations and, quite interestingly, being an instance of the solution of a non-trivial global problem by means of its local counterpart.
dc.description.firstpage578
dc.description.lastpage603
dc.description.volume615
dc.identifier.doi10.1016/j.ins.2022.10.045
dc.identifier.issn0020-0255
dc.identifier.urihttps://dspace.mackenzie.br/handle/10899/34288
dc.relation.ispartofInformation Sciences
dc.rightsAcesso Restrito
dc.subject.otherlanguageAutomata networks
dc.subject.otherlanguageConsensus
dc.subject.otherlanguageDecision problem
dc.subject.otherlanguageElementary cellular automata
dc.subject.otherlanguageEmergent computation
dc.subject.otherlanguageParity problem
dc.titleSynchronous solution of the parity problem on cyclic configurations, with elementary cellular automaton rule 150, over a family of directed, non-circulant, regular graphs
dc.typeArtigo
local.scopus.citations4
local.scopus.eid2-s2.0-85140077090
local.scopus.subjectAutomata networks
local.scopus.subjectAutomata rules
local.scopus.subjectCellular automatons
local.scopus.subjectCirculants
local.scopus.subjectConsensus
local.scopus.subjectDecision problems
local.scopus.subjectElementary cellular automaton
local.scopus.subjectEmergent computation
local.scopus.subjectParity problems
local.scopus.subjectRegular graphs
local.scopus.updated2024-12-01
local.scopus.urlhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85140077090&origin=inward
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