NXOR- or XOR-based robust template decomposition for cellular neural networks implementing an arbitrary Boolean function via support vector classifiers

Abstract

Robust template design for cellular neural networks (CNNs) implementing an arbitrary Boolean function is currently an active research area. If the given Boolean function is linearly separable, a single robust uncoupled CNN can be designed preferably as a maximal margin classifier to implement the Boolean function. On the other hand, if the linearly separable Boolean function has a small geometric margin or the Boolean function is not linearly separable, a popular approach is to find a sequence of robust uncoupled CNNs implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are usually restricted to assume only a given finite set of integers. In this study, we try to remove this unnecessary restriction. NXOR- or XOR-based decomposition algorithm utilizing the soft margin and maximal margin support vector classifiers is proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.