Derivation of Minimal Sums for Completely Specified Functions

Abstract

Some new concepts in switching theory are pre sented. One of these is called an "abridged minterm base." We can use an abridged minterm base instead of the minterm expansion in conventional absolute minimization procedures. Since an abridged minterm base almost always has much fewer minterms than are in the minterm expansion, we can derive an abridged minterm base for many functions for which it is impossible to derive the minterm expansion. This paper also introduces the concept of generalized inclusion function Q(f) and its decomposition theorem Q(g)·Q(h) = Q(g V h). The theorem is very useful.