O problema MODn com composição de autômatos celulares unidimensionais: resolução e simplificações

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dc.contributor.advisorOliveira, Pedro Paulo Balbi de
dc.contributor.advisor1Latteshttp://lattes.cnpq.br/9556738277476279por
dc.contributor.authorMartins, Claudio Luis de Meo
dc.creator.Latteshttp://lattes.cnpq.br/0498967801089430por
dc.date.accessioned2017-04-19T14:04:34Z
dc.date.accessioned2020-05-28T18:07:59Z
dc.date.available2020-05-28T18:07:59Z
dc.date.issued2016-08-24
dc.description.abstractThe understanding of how the composition of cellular automata rules can perform prede ned computations may contribute to the general notion of emerging computation by means of locally processing components. In this context, we propose a solution to the MODn Problem, which is the determination of whether the number of 1-bits in a binary string is perfectly divisible by the positive integer n > 1. The solution is a composition of one-dimensional cellular automata rules, i.e., the application of di erent rules on a lattice with periodic boundary conditions, which are replaced after some iterations, and all of them with maximum radius equal to n 􀀀 1. In this work, the (XU; LEE; CHAU, 2003) solution for MOD3 Problem (n = 3) is extended for any value of n, and the solution is given for any lattice size N that is co-prime to n. In this generalised solution, the number of iterations depends only on N, with O(N2). This solution relies upon two essential classes of rules, that have been de ned herein: the Replacement rules, that replace a certain amount of identical end bits on the lattice with the opposite value, and the Grouping rules, that group isolated strings of identical and consecutive bits on the lattice, to larger strings of the same bit value. Furthermore, we also show how the solution can be simpli- ed in terms of a reduction on the number of required rules, by de ning some operations that involve the rules' active state transitions, i.e., those that change the value of the centre cell of the neighbourhood. To this end, we de ned the operations of Partitioning (the separation of the active transitions of a rule in di erent rules), Joining (the union of the all active transitions of di erent rules in the same rule), and Merging (the joining of all active transitions of the rules involved, but removing some of them or even adding new active transitions to get the desired adjustments. Using the same concepts and methodology, we proposed a x for the only rule that had been reported in the literature for solving the MOD2 Problem, which is known as the Parity Problem.eng
dc.description.sponsorshipFundo Mackenzie de Pesquisapor
dc.formatapplication/pdf*
dc.identifier.citationMARTINS, Claudio Luis de Meo. O problema MODn com composição de autômatos celulares unidimensionais: resolução e simplificações. 2016. 93 f. Tese (Engenharia Elétrica) - Universidade Presbiteriana Mackenzie, São Paulo .por
dc.identifier.urihttp://dspace.mackenzie.br/handle/10899/24273
dc.keywordscellular automataeng
dc.keywordsemergent computationeng
dc.keywordsrule compositioneng
dc.keywordsmodulo-n problemeng
dc.keywordsactive state transitionseng
dc.languageporpor
dc.publisherUniversidade Presbiteriana Mackenziepor
dc.rightsAcesso Abertopor
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectautômatos celularespor
dc.subjectcomputação emergentepor
dc.subjectcomposição de regraspor
dc.subjectproblema módulo-npor
dc.subjecttransições de estado ativaspor
dc.subject.cnpqCNPQ::CIENCIAS EXATAS E DA TERRApor
dc.thumbnail.urlhttp://tede.mackenzie.br/jspui/retrieve/14050/CLAUDIO%20LUIS%20DE%20MEO%20MARTINS.pdf.jpg*
dc.titleO problema MODn com composição de autômatos celulares unidimensionais: resolução e simplificaçõespor
dc.typeTesepor
local.contributor.board1Monteiro, Luiz Henrique Alves
local.contributor.board1Latteshttp://lattes.cnpq.br/1820487447148268por
local.contributor.board2Mendonça, José Ricardo Gonçalves de
local.contributor.board2Latteshttp://lattes.cnpq.br/8792749813872106por
local.contributor.board3Barbosa, Valmir Carneiro
local.contributor.board3Latteshttp://lattes.cnpq.br/4602221579308599por
local.contributor.board4Silva, Leandro Augusto da
local.contributor.board4Latteshttp://lattes.cnpq.br/1396385111251741por
local.publisher.countryBrasilpor
local.publisher.departmentEscola de Engenharia Mackenzie (EE)por
local.publisher.initialsUPMpor
local.publisher.programEngenharia Elétricapor
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