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.\ud \ud 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.\ud \ud 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.\ud \ud 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

Distributed Branching Bisimulation Minimization by Inductive Signatures

We present a new distributed algorithm for state space minimization modulo branching bisimulation. Like its predecessor it uses signatures for refinement, but the refinement process and the signatures have been optimized to exploit the fact that the input graph contains no tau-loops. The optimization in the refinement process is meant to reduce both the number of iterations needed and the memory requirements. In the former case we cannot prove that there is an improvement, but our experiments show that in many cases the number of iterations is smaller. In the latter case, we can prove that the worst case memory use of the new algorithm is linear in the size of the state space, whereas the old algorithm has a quadratic upper bound. The paper includes a proof of correctness of the new algorithm and the results of a number of experiments that compare the performance of the old and the new algorithms

Distributed Branching Bisimulation Reduction of State Spaces

AbstractEnumerative model checking tools are limited by the size of the state space to which they can be applied. Reduction modulo branching bisimulation usually results in a much smaller state space and therefore enables model checking of much larger state spaces. We present an algorithm for reducing state spaces modulo branching bisimulation which is suitable for distributed implementation. The target architecture is a cluster with a high bandwidth interconnect. The algorithm is based on partition refinement and it works on transition systems which contain cycles of invisible steps, without eliminating strongly connected components first. To avoid fine grained parallelism, the algorithm refines the whole partition instead of just a single block in the partition. We prove correctness and also present some experimental results obtained with single threaded and distributed prototypes

Bisimulation minimisations for Boolean equation systems

Boolean equation systems (BESs) have been used to encode several complex verification problems, including model checking and equivalence checking. We introduce the concepts of strong bisimulation and oblivious bisimulation for BESs, and we prove that these can be used for minimising BESs prior to solving these. Our results show that large reductions of the BESs may be obtained efficiently. Minimisation is rewarding for BESs with non-trivial alternations: the time required for solving the original BES exceeds the time required for quotienting plus the time for solving the quotient. Furthermore, we provide a verification example that demonstrates that bisimulation minimisation of a process prior to encoding the verification problem on that process as a BES can be arbitrarily less effective than minimising the BES that encodes the verification problem

Proceedings of SUMo and CompoNet 2011

International audienc

Compositional Verification of Priority Systems using Sharp Bisimulation

Sharp bisimulation is a refinement of divergence-preserving branching (a.k.a. divbranching) bisimulation, parameterized by a subset of the system's actions, called strong actions. This parameterization allows the sharp bisimulation to be tailored by the property under verification, whichever property of the modal µ-calculus is considered, while potentially reducing more than strong bisimulation. Sharp bisimulation equivalence is a congruence for parallel composition and other process algebraic operators such as hide, cut, and rename, and hence can be used in a compositional verification setting. In this paper, we prove that sharp bisimulation equivalence is also a congruence for action priority operators under some conditions on strong actions. We compare sharp bisimulation with orthogonal bisimulation, whose equivalence is also a congruence for action priority. We show that, if the internal action τ neither yield priority to nor take priority over other actions, then the quotient of a system with respect to sharp bisimulation equivalence (called sharp minimization) cannot be larger than the quotient of the same system with respect to orthogonal bisimulation equivalence. We then describe a signature-based partition refinement algorithm for sharp minimization, implemented in the BCG MIN tool of the CADP software toolbox. This algorithm can be adapted to implement orthogonal minimization. We show on a crafted example that using compositional sharp minimization may yield state space reductions that outperform compositional orthogonal minimization by several orders of magnitude. Finally, we illustrate the use of sharp minimization and priority to verify a bully leader election algorithm

Bisimulation minimisations for boolean equation systems

Abstract. Boolean equation systems (BESs) have been used to encode several complex verification problems, including model checking and equivalence checking. We introduce the concepts of strong bisimulation and idempotence-identifying bisimulation for BESs, and we prove that these can be used for minimising BESs prior to solving these. Our results show that large reductions of the BESs may be obtained efficiently. Minimisation is rewarding for BESs with non-trivial alternations: the time required for solving the original BES mostly exceeds the time required for quotienting plus the time for solving the quotient. Furthermore, we provide a verification example that demonstrates that bisimulation minimisation of a process prior to encoding the verification problem on that process as a BES can be arbitrarily less effective than minimising the BES that encodes the verification problem