Obtenção e utilização de grafos-limite de autômatos celulares elementares
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Tipo
Tese
Data de publicação
2016-09-28
Periódico
Citações (Scopus)
Autores
Ruivo, Eurico Luiz Prospero
Orientador
Oliveira, Pedro Paulo Balbi de
Título da Revista
ISSN da Revista
Título de Volume
Membros da banca
Silva, Leandro Nunes de Castro
Omar, Nizam
Mandel, Arnaldo
Chacc, Eric Antonio Goles
Omar, Nizam
Mandel, Arnaldo
Chacc, Eric Antonio Goles
Programa
Engenharia Elétrica
Resumo
Cellular automata are locally de ned dynamical systems which are discrete in space, time
and in the state variables, and capable of presenting arbitrarily complex global emergent
behaviour. One core question in the study of cellular automata refers to their limit behaviour,
that is, to the global dynamical features in a in nite time evolution. Previous works
have shown that for nite time evolutions, one-dimensional cellular automata present dynamics
which can be described by regular languages and, therefore, by nite automata.
Also, such studies have shown the existence of growth patterns in the evolution of such
nite automata for some cellular automata rules; however these results were obtained manually
by directly inspecting the structures that arise during the time evolution. In this
work we present the formalisation of an automatic method to compute such structures.
Based on this, the rules of the elementary cellular automata rule space were classi ed according
to the existence of a growth pattern in their nite automata. Also, we present new
methods to infer the limit graph of some elementary cellular automata rules by analysing
the regular expressions describing their behaviour in nite-time and the attractors of each
rule, as well as an application of these graphs in computing the Fourier spectra of the rules.
Descrição
Palavras-chave
autômatos celulares elementares , comportamento limite , grafos de complexo , isomorfismo entre grafos , linguagem regular , transformada discreta de Fourier
Assuntos Scopus
Citação
RUIVO, Eurico Luiz Prospero. Obtenção e utilização de grafos-limite de autômatos celulares elementares. 2016. 111 f. Tese( Engenharia Elétrica) - Universidade Presbiteriana Mackenzie, São Paulo .