Algoritmo de Lempel-Ziv aplicado à classificação quantitativa de autômatos celulares
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 Wol...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | Brasil |
| Institución: | Universidade Federal de Uberlândia (UFU) |
| Repositorio: | Repositório Institucional da UFU |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufu.br:123456789/15670 |
| Acceso en línea: | https://repositorio.ufu.br/handle/123456789/15670 https://doi.org/10.14393/ufu.di.2014.528 |
| Access Level: | acceso abierto |
| Palabra clave: | 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 |
| Sumario: | 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. |
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