Analysis of Algorithms for Computation of Direct Partial Logic Derivatives in Multiple-Valued Decision Diagrams

Abstract

Reliability is a very important characteristic of many systems. However, there are some problems how to represent a complex system that contains a lot of different components. The problem of component variability can be solved by using Multi-State Systems (MSSs), which consists of components with different number of performance levels. The problem of large system dimension can be solved by using decision diagrams for system representation. However, new algorithms have to be developed for reliability analysis of MSSs represented by decision diagrams. A possible way is the extension of existing tools of reliability analysis on this representation of a MSS. Direct Partial Logic Derivatives (Direct Partial Logic Derivatives) are one of the tools that have been expanded on decision diagrams. Direct Partial Logic Derivatives can be used in reliability analysis to model the consequence of the component performance change on the system performance. Therefore, they can be used to find components that have the most influence on the system reliability. In some papers, there have been proposed algorithms that can be used to compute Direct Partial Logic Derivatives from decision diagrams. However, their computational complexity has not been yet studied. In this paper, we summarize these algorithms and analyze their time complexity using some benchmarks that are often used to compare the complexity of algorithms designed for logic synthesis.