Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Symbolic model checking for real-time systems
Information and Computation
Model checking
An abstract Monte-Carlo method for the analysis of probabilistic programs
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Probabilistic symbolic model checking with PRISM: a hybrid approach
International Journal on Software Tools for Technology Transfer (STTT) - Special section on tools and algorithms for the construction and analysis of systems
Statistical probabilistic model checking with a focus on time-bounded properties
Information and Computation
Splitting for rare-event simulation
Proceedings of the 38th conference on Winter simulation
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Statistical Model Checking Using Perfect Simulation
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
Approximate Model Checking of PCTL Involving Unbounded Path Properties
ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
Error control for probabilistic model checking
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
On statistical model checking of stochastic systems
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Ymer: a statistical model checker
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Statistical model checking for cyber-physical systems
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Rare-event verification for stochastic hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Learning stochastic timed automata from sample executions
ISoLA'12 Proceedings of the 5th international conference on Leveraging Applications of Formal Methods, Verification and Validation: technologies for mastering change - Volume Part I
Automated reliability estimation over partial systematic explorations
Proceedings of the 2013 International Conference on Software Engineering
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We consider statistical (sampling-based) solution methods for verifying probabilistic properties with unbounded until. Statistical solution methods for probabilistic verification use sample execution trajectories for a system to verify properties with some level of confidence. The main challenge with properties that are expressed using unbounded until is to ensure termination in the face of potentially infinite sample execution trajectories. We describe two alternative solution methods, each one with its own merits. The first method relies on reachability analysis, and is suitable primarily for large Markov chains where reachability analysis can be performed efficiently using symbolic data structures, but for which numerical probability computations are expensive. The second method employs a termination probability and weighted sampling. This method does not rely on any specific structure of the model, but error control is more challenging. We show how the choice of termination probability--when applied to Markov chains--is tied to the subdominant eigenvalue of the transition probability matrix, which relates it to iterative numerical solution techniques for the same problem.