Minimal sums for Boolean functions having many unspecified fundamental products

Many techniques have been developed for finding minimal sums and minimal products for Boolean functions. In all of these techniques, it is necessary to use either all of the fundamental products which must be included in the function and all of the unspecified fundamental products ("don\´t cares") or all of the fundamental products which must not be included in the function and all of the unspecified fundamental products. There is a class of problems which can be specified very simply, but in practice cannot be solved using existing techniques. This class consists of those problems for which almost all of the fundamental products are unspecified. These problems can be described by specifying the fundamental products to be included in the function- the 1-terms - and the fundamental products to be excluded from the function - the 0-terms. Techniques for forming minimal sums and products have been developed which require use of only the 1-terms and the 0-terms. This specification can be in either canonical or non-canonical form. In addition, a modification of this basic technique has been developed which permits the direct generation of only the essential prime implicants. The extension of the basic technique to multiple-output networks is also described.