Synthesis of Bases of Boolean Functions Based on Post Classes

Abstract

The paper introduced the concept of Post's characteristic of Boolean functions. Five-dimensional Post's cube has been constructed. All empty Post's classes are described, and nonempty classes form the Post's lattice. An algorithm of finding the base's systems of Boolean function has been presented, and Post's characteristics have been found. Formulas for calculating the number of two-functional, three-functional, and four-functional bases of an arbitrary system of Boolean functions are obtained. The results for the class of Boolean functions arnost equals two, three, and four, indicating the exact number of one-functional, two-functional, three-functional, and four-function bases. This paper uses Boolean functions in tables, graphs, n-dimensional cubes. Boolean functions are also presented analytically based on formulas of Boolean algebras. This is required to find of bases of Boolean functions with Post's characteristic, performed by a developed software package to analyze Boolean functions.