Importance sampling for the simulation of highly reliable Markovian systems
Management Science
Model checking
POPL '81 Proceedings of the 8th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Multilevel Splitting for Estimating Rare Event Probabilities
Operations Research
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Sequential Monte Carlo for rare event estimation
Statistics and Computing
Coupling and importance sampling for statistical model checking
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
A platform for high performance statistical model checking --- PLASMA
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Rare event simulation for highly dependable systems with fast repairs
Performance Evaluation
Cross-entropy optimisation of importance sampling parameters for statistical model checking
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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Statistical model checking avoids the intractable growth of states associated with probabilistic model checking by estimating the probability of a property from simulations. Rare properties are often important, but pose a challenge for simulation-based approaches: the relative error of the estimate is unbounded. A key objective for statistical model checking rare events is thus to reduce the variance of the estimator. Importance splitting achieves this by estimating a sequence of conditional probabilities, whose product is the required result. To apply this idea to model checking it is necessary to define a score function based on logical properties, and a set of levels that delimit the conditional probabilities. In this paper we motivate the use of importance splitting for statistical model checking and describe the necessary and desirable properties of score functions and levels. We illustrate how a score function may be derived from a property and give two importance splitting algorithms: one that uses fixed levels and one that discovers optimal levels adaptively.