Minimal Cut Sets and Path Sets in Binary Decision Diagrams and logical differential calculus

Abstract

Reliability is an important characteristic of many systems. One of the important steps of reliability analysis is the representation and mathematical description of the analyzed system. Binary Decision Diagrams (BDDs) are very convenient for representation of large systems, because they can be processed on computers efficiently. The application of this technique in reliability analysis requires the development of new methods that can be applied on this structure (representation). Some of the most popular tools of reliability engineering are methods based on Minimal Cut Sets (MCSs) or Minimal Path Sets (MPSs). However, these methods are based on the assumption that MCSs (MPSs) are known a priori. Therefore, the development of methods for definition of MCSs (MPSs) based on a BDD is actual problem in reliability analysis. In this paper, we investigate the relation between BDDs and MCSs (MPSs) and proposed a new algorithm that can be used to detect all MCSs (MPSs) in a BDD. Our approach is based on the use of logical differential calculus, especially one of its parts that is known as a direct partial logic derivative.