Abstract—There are several algorithms that determine directly an irredundant normal form (INF) of a Boolean function without generating the entire set of prime implicants. These algorithms can generate solutions for the minimization problem much more rapidly than the algorithms determining minimum normal forms (MNF), and the cost of these solutions is, in many cases, very close to the minimum.

Abstract—An algorithm for multithreshold threshold element synthesis, generalizing Haring's "run measure minimization" algorithm, is presented. The algorithm is based on the possibility of assigning equal weights to variables in a symmetry group of a given Boolean function (for totally or partially symmetric Boolean functions). Thus, although a supplementary operation is required for determining the symmetry group of the Boolean functions, both an important reduction in the number of tests required to minimize the number of thresholds and a more economic solution are assured, when synthesizing totally or partially symmetric Boolean functions.

In this correspondence it is shown that by applying Gavrilov's test algorithm to any Boolean function numerically represented by its'' constrained designation numbers'', introduced by Ledley, a very suitable program for the automatic determination of the prime implicants and of the prime implicant table can be established.