Algoritmo de Lempel-Ziv aplicado à classificação quantitativa de autômatos celulares

• Ano de defesa: 2014
• Autor(a) principal: Nunes, Ciro Alves Justino
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; BR; Programa de Pós-graduação em Física; Ciências Exatas e da Terra; UFU
• Palavras-chave em Português: Autômatos celulares; Complexidade de Lempel-Ziv; Fonte ergódica; Teoria da informação; Entropia algorítmica; Sólidos complexos; Cristalografia; Dimensão fractal; Fatorização; Aleatoriedade; Cadeias de dados; Cellular automata; Lempel-Ziv complexity; Ergodic source; Information theory; Algorithmic entropy; Crystallography; Crystallographically challenging solids; Fractal dimension; Factorization; Randomness; Strings; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA
• Link de acesso: https://repositorio.ufu.br/handle/123456789/15670; https://doi.org/10.14393/ufu.di.2014.528

This work presents the so-called elementary Cellular Automata according to the principles of the Lempel-Ziv (LZ76) algorithm applied to binary sequences. We aim at organizing them quantitatively in agreement with the complexity of updating the states, and by relating the data arrangements to the Wolfram s Classification. In this way, Complexity Classes can classify such machines. Further, sequences with maximum LZ complexity - MLZs - and their properties will be presented and discussed. The latter will be useful to characterize the truly random ergodic emissions, thus to understand the degree of randomness of the rules governing automata. The above treatment will be extended to problems of crystal defects in crystallographically challenging solids (with intermediate atomic order between the ideal long-range crystallinity and amorphicity), by using tools from information theory.