Em busca de um algoritmo construtivo para autômatos celulares reversíveis: a abordagem das regras primitivas e derivadas

• Ano de defesa: 2008
• Autor(a) principal: Kronemberger, Guilherme
• Orientador(a): Oliveira, Pedro Paulo Balbi de
• Banca de defesa: Monteiro, Luiz Henrique Alves , Carvalho, André Carlos Ponce de Leon Ferreira de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Presbiteriana Mackenzie
• Programa de Pós-Graduação: Engenharia Elétrica
• Departamento: Engenharia Elétrica
• País: BR
• Palavras-chave em Português: autômato celular; autômato celular reversível; NKS; computação reversível
• Palavras-chave em Inglês: cellular automata; reversible cellular automata; NKS; reversible computation
• Área do conhecimento CNPq: CNPQ::ENGENHARIAS::ENGENHARIA ELETRICA
• Link de acesso: http://dspace.mackenzie.br/handle/10899/24398

Cellular automata have been studied as computer models in many different areas. They have many properties, one of them being reversibility. Reversible cellular automata can be used, among other applications, for data compressing and encryption. Apparently, the reversible rules featured in the literature seem to have been derived through exhaustive searches in their corresponding spaces. However, it would be important the availability of an algorithm that would allow their direct and easy construction, different from what occurs in literature. This is the aim of this work. Along this line, we tried to come up with an algorithm to allow the identification of one-dimensional, reversible cellular automaton rules. This was based on reversible rules with 2 states and 2, 3, 4 and 5 cells per neighborhood, and on those with 3 states and 2 and 3 cells per neighborhood, all of them drawn out of exhaustive analysis and from the literature. By studying these rules it was possible to verify in each space that: all reversible rules are balanced; they are symmetrically distributed; a subset of them herein denoted primitive reversible rules, RPs have a simple formation law, defined by homogeneous blocks of states; and, if a rule is reversible, so are all its dynamically equivalent rules. In the attempt to obtain the targetted algorithm, an approach was explored in which the non-primitive reversible rules (the so-called derived rules, RDs) were supposed to be obtained from the primitives. Along this line, two ways to construct the RDs were tried out, one based upon using all RPs jointly as a group, and another, using them individually; however, neither of them led to a positive result. Additionally, relations between the properties of reversibility and conservativity of a rule have also been studied in the rule spaces considered.