One Approach to synthesizing predicate circuits on the basis of generalized variables

Abstract

The asymptotic behavior of the Shannon’s function LB(n) is studied for complexity of n-variable predicate implementation with the use of predicate circuits over arbitrary complete basis B. A new definition of the reduced weight of the predicate is introduced, regarding it as a solution of a specific linear programming problem based on a system of predicate’s generalized variables. New, more exact upper elements for LB(n) in a number of bases are acquired by the means of special decompositions of initial predicates using universal sets of predicates constructed for circuits consisting of bases elements with minimal reduced weight.