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

Abstract

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.