CNN Genes for One-Dimensional Cellular Automata: A Multi-Nested Piecewise-Linear Approach

Abstract

This paper introduces a novel CNN cell which guarantees the implementation of any local rule on three variables defined by a Boolean truth table. Moreover, since the output of the cell is completely specified by a simple mathematical formula, it is possible to develop a systematic theory for locating those regions in the CNN genes parameter space where complex behaviors may occur. The output cell formula is a simple piecewise-linear function, and for the case of a one-dimensional CNN the entire set of 256 CNN genes associated with the corresponding local Boolean functions are listed in this paper.