Canonical restricted mixed-polarity exclusive sums of products

The concept of canonical restricted mixed polarity (CRMP) exclusive sum of products (ESOP) forms is introduced. It includes the inconsistent canonical Reed-Muller and generalized Reed-Muller forms as special cases. The set of CRMP forms is included in the set of ESOP expressions. An attempt to characterize minimal CRMP forms for completely specified Boolean functions is presented, as well as an attempt to gain insight into the complexity of computation needed to find such a form. Some fundamental properties unique to CRMPs are proved. It is also proved that the upper bound on the number of terms in the CRMP form is smaller than that in the conventional normal forms and is equal to that of the ESOPs. A theorem providing a lower bound on the number of CRMP terms is also given. These results prove the validity of the CRMP concept. An efficient generic heuristic algorithm to find the CRMP form is presented.<
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