Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking

The verification of quantitative aspects like performance and dependability by means of model checking has become an important and vivid area of research over the past decade. An important result of that research is the logic CSL (continuous stochastic logic) and its corresponding model checking algorithms. The evaluation of properties expressed in CSL makes it necessary to solve large systems of linear (differential) equations, usually by means of numerical analysis. Both the inherent time and space complexity of the numerical algorithms make it practically infeasible to model check systems with more than 100 million states, whereas realistic system models may have billions of states. To overcome this severe restriction, it is important to be able to replace the original state space with a probabilistically equivalent, but smaller one. The most prominent equivalence relation is bisimulation, for which also a stochastic variant exists (Markovian bisimulation). In many cases, this bisimulation allows for a substantial reduction of the state space size. But, these savings in space come at the cost of an increased time complexity. Therefore in this paper a new distributed signature-based algorithm for the computation of the bisimulation quotient of a given state space is introduced. To demonstrate the feasibility of our approach in both a sequential, and more important, in a distributed setting, we have performed a number of case studies.