Logic Properties of Unate Discrete and Switching Functions

The total and local unateness of discrete and of switching functions are studied from a theoretical point of view. One shows that the local unateness leads to the concept of hazard-free transition for a discrete function. Unate covers for discrete functions are defined: they are either the smallest unate functions larger than a discrete function, or the largest unate functions smaller than a discrete function. These concepts play a key role in hazard-free design of multiple-valued networks. Three-level types of multiple-valued networks using MIN and MAX gates are presented. These networks improve, from a hazard point of view the well known two-level networks presented by Eichel-berger in the frame of switching theory.