An exact algorithm to minimize mixed-radix exclusive sums of products for incompletely specified Boolean functions

An exact algorithm for the synthesis of mixed polarity exclusive sum of product (ESOP) expressions for arbitrary size incompletely specified Boolean functions is presented. For more than four input variables, this problem has not been solved yet. A decision function H is constructed for a Boolean function f that describes all possible ESOP solutions to f. The function H plays for the ESOP minimization problem a role analogous to that of the Petrick function for the minimization of the inclusive sum of product expression problem of classical logic. Each product of literals that satisfies the function H corresponds to one ESOP solution of f. The algorithms to create and solve function H are presented.<>