The Generalization of WOSF and Corresponding Outputs

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 use minimum weight vectors as base vectors to build all global classes of same order and characterize WOSF to generalize three properties of global classes. Finally, we propose 3 translated formulas to fast generate corresponding outputs of BF equivalent classes, not perform extra machine training or mathematical computation.