Solving the parity problem in one-dimensional cellular automata

Página do item simplificado
dc.contributor.authorBetel H.
dc.contributor.authorDe Oliveira P.P.B.
dc.contributor.authorFlocchini P.
dc.date.accessioned2024-03-13T01:03:56Z
dc.date.available2024-03-13T01:03:56Z
dc.date.issued2013
dc.description.abstractThe parity problem is a well-known benchmark task in various areas of computer science. Here we consider its version for one-dimensional, binary cellular automata, with periodic boundary conditions: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. Since the problem is ill-defined for even-sized lattices (which, by definition, would never be able to converge to 1), it suffices to account for odd-sized lattices only. We are interested in determining the minimal neighbourhood size that allows the problem to be solvable for any arbitrary initial configuration. On the one hand, we show that radius 2 is not sufficient, proving that there exists no radius 2 rule that can solve the parity problem, even in the simpler case of prime-sized lattices. On the other hand, we design a radius 4 rule that converges correctly for any initial configuration and formally prove its correctness. Whether or not there exists a radius 3 rule that solves the parity problem remains an open problem; however, we review recent data against a solution in radius 3, thus providing strong empirical evidence that there may not exist a radius 3 solution even for prime-sized lattices only, contrary to a recent conjecture in the literature. © 2013 Springer Science+Business Media Dordrecht.
dc.description.firstpage323
dc.description.issuenumber3
dc.description.lastpage337
dc.description.volume12
dc.identifier.doi10.1007/s11047-013-9374-9
dc.identifier.issn1567-7818
dc.identifier.urihttps://dspace.mackenzie.br/handle/10899/36574
dc.relation.ispartofNatural Computing
dc.rightsAcesso Restrito
dc.subject.otherlanguageDe Bruijn graphs
dc.subject.otherlanguageDensity classification
dc.subject.otherlanguageElementary cellular automata
dc.subject.otherlanguageEmergent computation
dc.subject.otherlanguageParity problem
dc.titleSolving the parity problem in one-dimensional cellular automata
dc.typeArtigo de evento
local.scopus.citations22
local.scopus.eid2-s2.0-84882455435
local.scopus.subjectDe Bruijn graphs
local.scopus.subjectDensity classifications
local.scopus.subjectElementary cellular automaton
local.scopus.subjectEmergent computation
local.scopus.subjectParity problems
local.scopus.updated2024-05-01
local.scopus.urlhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84882455435&origin=inward
Arquivos
Coleções
Artigo de evento