A Search of WOSF Equivalent Classes up to Order 5

Abstract

Weighted order statistic filters (WOSF) generate linearly separable Boolean functions. In some cases, 2 different WOSF may generate the same Boolean function. We thus can collect all of the WOSF together, which generate the same Boolean function. In this paper, we construct equivalent classes of WOSF, the BF equivalent class and the global equivalent class. Besides, we generalize three properties of the global classes and collect minimum weight vectors to build the global classes.