Dynamic Dependability Analysis of Shuffle-exchange Networks using HOL Theorem Proving

Abstract: Dynamic dependability models, such as dynamic fault trees (DFTs) and dynamic reliability block diagrams (DRBDs), are introduced to overcome the modeling limitations of traditional models. Recently, higher-order logic (HOL) formalizations of both models have been conducted, which allow the analysis of these models formally, within a theorem prover. In this report, we provide the formal dynamic dependability analysis of shuffle-exchange networks, which are multistage interconnection networks that are commonly used in multiprocessor systems. We use DFTs and DRBDs to model the terminal, broadcast and network reliability with dynamic spare gates and constructs in several generic versions. We verify generic expressions of probability of failure and reliability of these systems, which can be instantiated with any number of system components and failure rates to reason about the failure behavior of these networks.