Discovery of the boolean functions to the best density-classification rules using gene expression programming

Abstract

Cellular automata are idealized versions of massively parallel, decentralized computing systems capable of emergent behaviors. These complex behaviors result from the simultaneous execution of simple rules at multiple local sites. A widely studied behavior consists of correctly determining the density of an initial configuration, and both human and computer-written rules have been found that perform with high efficiency at this task. However, the two best rules for the density-classification task, Coevolution1 and Coevolution2, were discovered using a coevolutionary algorithm in which a genetic algorithm evolved the rules and, therefore, only the output bits of the rules are known. However, to understand why these and other rules perform so well and how the information is transmitted throughout the cellular automata, the Boolean expressions that orchestrate this behavior must be known. The results presented in this work are a contribution in that direction.