Realization of Boolean Functions and Gene Bank of Cellular Neural Networks

A paradigm for nonlinear spatial-temporal processing, cellular neural networks (CNN), was created by inspiration from the cellular automata and neural networks. This article is an exploration of the important aspect of realizing Boolean functions by using standard CNN. A neat CNN truth table of n binary variables and an essential formula of an uncoupled CNN are discovered, and an effective method of realizing all linearly separable Boolean functions (LSBF) via CNN is proposed. Borrowed from biological concepts and terms, the parameter group in a CNN is a metaphor for gene which completely determines the dynamical properties of the CNN. The CNN gene bank, which consists of the family of all linearly separable Boolean genes (LSBG) that are associated with all the LSBF, can be easily determined and progressively established. An interesting phenomenon is that the number of LSBG with the von Neumann neighborhood is 94572, which is close to the number of genes existing in the human genome.