Complete Description of Adjacent Classes of Boolean Algebras by Basis Equivalence

Abstract

The theory of logical functions is the basis of many intelligent systems based on using different sets of bases. The paper has proposed considering the Boolean functions theory from the view of universal Boolean algebra. The set of bases S can be constructed in a Boolean algebra with a preset signature. The problem is solved for which collections of bases S exist algebras which have those and only those collections of bases. The division of the set of Boolean algebras M into adjacent classes, which are determined by the codes of canonical algebras, is received based on the introduced concept of basis equivalence. Tables are presented where all adjacent classes are described by basis equivalence, and a grating of these classes is constructed. Since grating has 1060 vertexes and 4804 edges, the most exciting fragments are presented.