A method of determination of all the minimal forms of Boolean functions

Abstract

A method of minimization of Boolean functions is described. Though directly concerned with the evaluation of the minimal sum of products, it can be easily extended to obtain the minimal product of sums. It has been shown that, after the selection of the essential prime implicants, there exists a ‘row-merger’ step or a ‘row-merger’ and ‘row-cancellation’ step which reveals many alternative covers. The method of obtaining the solution for the cyclic prime implicant matrix has been systematized by introducing the ‘irredundant S^at-set’ and the ‘perturbation set’ of the prime implicants. The method yields all the minimal sums, however complex the problem may be.