Probabilistic Verification of Discrete Event Systems Using Acceptance Sampling
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Numerical vs. statistical probabilistic model checking
International Journal on Software Tools for Technology Transfer (STTT)
Statistical probabilistic model checking with a focus on time-bounded properties
Information and Computation
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
A Bayesian Approach to Model Checking Biological Systems
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Rare Event Simulation using Monte Carlo Methods
Rare Event Simulation using Monte Carlo Methods
Bayesian statistical model checking with application to Simulink/Stateflow verification
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Statistical verification of probabilistic properties with unbounded until
SBMF'10 Proceedings of the 13th Brazilian conference on Formal methods: foundations and applications
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Statistical model checking qos properties of systems with SBIP
ISoLA'12 Proceedings of the 5th international conference on Leveraging Applications of Formal Methods, Verification and Validation: technologies for mastering change - Volume Part I
Rewarding probabilistic hybrid automata
Proceedings of the 16th international conference on Hybrid systems: computation and control
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In this paper we address the problem of verifying in stochastic hybrid systems temporal logic properties whose probability of being true is very small --- rare events. It is well known that sampling-based (Monte Carlo) techniques, such as statistical model checking, do not perform well for estimating rare-event probabilities. The problem is that the sample size required for good accuracy grows too large as the event probability tends to zero. However, several techniques have been developed to address this problem. We focus on importance sampling techniques, which bias the original system to compute highly accurate and efficient estimates. The main difficulty in importance sampling is to devise a good biasing density, that is, a density yielding a low-variance estimator. In this paper, we show how to use the cross-entropy method for generating approximately optimal biasing densities for statistical model checking. We apply the method with importance sampling and statistical model checking for estimating rare-event probabilities in stochastic hybrid systems coded as Stateflow/Simulink diagrams.