Topological Equivalence Classification of Balanced Linearly Separable Boolean Functions on n-Dimensional Hypercube

Abstract

The concept of conformal transformation is proposed through the study of the spatial structure of [Formula: see text]-dimensional hypercubes. Based on conformal transformation, a novel algorithm, called topological equivalence classification algorithm, is proposed for classifying balanced linearly separable Boolean functions. By the proposed algorithm, the topological equivalence classes of all balanced linearly separable Boolean functions and the number of Boolean functions in each of the topological equivalence classes are obtained. In addition, the properties of conformal transformation also show an application prospect for decomposing nonlinearly separable Boolean functions.