Average Values of Quantities Appearing in Boolean Function Minimization

Abstract

In connection with the problem of two-level minimization of Boolean functions, we have obtained in a combinatorial way the formulas which give the following quantities of statistical interest: average numbers of k cubes, prime k cubes and essential k cubes of a Boolean function. The parameters which appear in our formulas are: number of variables, number of ``one'' vertices and number of ``don't care'' vertices.