Algumas propriedades de autômatos celulares unidimensionais conservativos e reversíveis

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dc.contributor.advisorOliveira, Pedro Paulo Balbi dept_BR
dc.contributor.advisor1Latteshttp://lattes.cnpq.br/9556738277476279por
dc.contributor.authorOliveira, Angelo Schranko dept_BR
dc.creator.Latteshttp://lattes.cnpq.br/3426939060925235por
dc.date.accessioned2016-04-18T21:39:48Z
dc.date.accessioned2020-05-28T18:08:47Z
dc.date.available2009-02-26pt_BR
dc.date.available2020-05-28T18:08:47Z
dc.date.issued2009-01-28pt_BR
dc.description.abstractCellular automata (CAs) can be defined as discrete dynamical systems over n-dimensional networks of locally connected components, whose evolution occur in a discrete, synchronous and homogeneous fashion. Among their several applications, they have been used as a tool for complex systems modeling governed by fundamental laws of conservation (number-conserving cellular automata) or reversibility (reversible cellular automata). Another fundamental property that can be observed in CAs is regarding to their linearity (linear cellular automata) or nonlinearity. Usually, linear phenomena present low dynamic complexity, however, nonlinear phenoma can present complex behaviours like sensitive dependence on initial conditions and routes to chaos. This work focuses on investigating properties of cellular automata belonging to the intersection of those four classes, namely, reversible, number-conserving, and linear or nonlinear cellular automata. After presenting basic definitions, the notions of number-conserving cellular automata, conservation degree and reversibility are reviewed. Following, a dynamical characterisation parameter which relates the reversibility property of a onedimensional cellular automaton and the pre-images of their basic blocks is introduced, and some proofs of its general properties are given. Empirical observations herein suggest that a cellular automaton is reversible and number-conserving if, and only if, its local transition function is a composition of the local transition functions of the reversible, number-conserving cellular automata with neighbourhood size n=2; such an observation was drawn for neighbourhood sizes n∈{2, 3, 4, 5, 6} and number of states q=2; n∈{2, 3} and q=3; n∈{2, 3} and q=4. A proof for such a conjecture would allow the enumeration between neighbourhood lengths and the quantity of reversible, numberconserving cellular automata in the corresponding space, which can be easily identified by working out the compositions of the local transition functions with n=2. Finally, some relationships between reversible, number-conserving, linear and nonlinear CA rules, their spatio-temporal diagrams and basin of attraction fields are presented.eng
dc.description.sponsorshipWolfram Research, Inc.pt_BR
dc.formatapplication/pdfpor
dc.identifier.citationOLIVEIRA, Angelo Schranko de. Algumas propriedades de autômatos celulares unidimensionais conservativos e reversíveis. 2009. 71 f. Dissertação (Mestrado em Engenharia Elétrica) - Universidade Presbiteriana Mackenzie, São Paulo, 2009.por
dc.identifier.urihttp://dspace.mackenzie.br/handle/10899/24433
dc.languageporpor
dc.publisherUniversidade Presbiteriana Mackenziepor
dc.rightsAcesso Abertopor
dc.subjectautômato celularpor
dc.subjectconservabilidadepor
dc.subjectreversibilidadepor
dc.subjectnão-linearidadepor
dc.subjectsistema dinâmico discretopor
dc.subjectNKSpor
dc.subjectcellular automatoneng
dc.subjectconservativityeng
dc.subjectreversibilityeng
dc.subjectnonlinearityeng
dc.subjectdiscrete dynamical systemeng
dc.subjectNKSeng
dc.subject.cnpqCNPQ::ENGENHARIAS::ENGENHARIA ELETRICApor
dc.titleAlgumas propriedades de autômatos celulares unidimensionais conservativos e reversíveispor
dc.typeDissertaçãopor
local.contributor.board1Silva, Leandro Nunes de Castropt_BR
local.contributor.board1Latteshttp://lattes.cnpq.br/2741458816539568por
local.contributor.board2Macau, Elbert Einstein Nehrerpt_BR
local.contributor.board2Latteshttp://lattes.cnpq.br/0793627832164040por
local.publisher.countryBRpor
local.publisher.departmentEngenharia Elétricapor
local.publisher.initialsUPMpor
local.publisher.programEngenharia Elétricapor
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