Generating Monotone Boolean Functions Using Hasse Diagram

Boolean functions play an important role in numerous research areas. One of the areas is reliability analysis where researchers frequently use Boolean functions to describe the relation of a system state to the state of its components. The functions they encounter are often monotone, due to the properties of the systems. Design, verification, and testing of reliability analysis algorithms often involve an examination of numerous functions. Therefore, in this paper, we describe an algorithm that generates all monotone Boolean functions of
$n$
variables utilizing relations defined by a Hasse diagram. Furthermore, we describe a way to experimentally verify the correctness of the implementation of such an algorithm—and similar algorithms—by using logic differential calculus and binary decision diagrams.