A New Method for Symmetry Recognition in Boolean Functions Based on the Set-Theoretical Logic Differentiation. I

Abstract

The paper presents a new method for the recognition of the different types of total and partial symmetry in boolean functions based on the numeric set-theoretical differentiation. The proposed algorithm is based on the theorem on the recognition of different types of partial symmetry. This algorithm, compared to the known, has a relatively less computational complexity of realization due to a comparatively smaller number of operations and procedures necessary for the accomplishment of the given task. This is proved by the presented examples for the recognition of the proposed method of the different types of symmetry in complete and incomplete of Boolean functions, including given in the SOP format, taken for comparison reasons from publications of the wellknown authors.