The complexity of probabilistic verification
Journal of the ACM (JACM)
Crowds: anonymity for Web transactions
ACM Transactions on Information and System Security (TISSEC)
Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Verifying Continuous Time Markov Chains
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
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)
A formal analysis of bluetooth device discovery
International Journal on Software Tools for Technology Transfer (STTT)
Statistical probabilistic model checking with a focus on time-bounded properties
Information and Computation
Analysis of probabilistic contract signing
Journal of Computer Security
Using probabilistic model checking in systems biology
ACM SIGMETRICS Performance Evaluation Review
Specification patterns for probabilistic quality properties
Proceedings of the 30th international conference on Software engineering
Simulation-Based CTMC Model Checking: An Empirical Evaluation
QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
Statistical Model Checking Using Perfect Simulation
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
How fast and fat is your probabilistic model checker? an experimental performance comparison
HVC'07 Proceedings of the 3rd international Haifa verification conference on Hardware and software: verification and testing
A bounded statistical approach for model checking of unbounded until properties
Proceedings of the IEEE/ACM international conference on Automated software engineering
Statistical model checking: an overview
RV'10 Proceedings of the First international conference on Runtime verification
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Improved probabilistic models for 802.11 protocol verification
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
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
PRISM: a tool for automatic verification of probabilistic systems
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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We have developed a new approximate probabilistic model-checking method for untimed properties in probabilistic systems, expressed in a probabilistic temporal logic (PCTL, CSL). This method, in contrast to the existing ones, does not require the untimed until properties to be bounded a priori, where the bound refers to the number of discrete steps in the system required to verify the until property. The method consists of two phases. In the first phase, a suitable system- and property-dependent bound k0 is obtained automatically. In the second phase, the probability of satisfying the k0-bounded until property is computed as the estimate of the probability of satisfying the original unbounded until property. Both phases require only verification of bounded until properties, which can be effectively performed by simulation-based methods. We prove the correctness of the proposed two-phase method and present its optimized implementation in the widely used PRISM model-checking engine. We compare this implementation with sampling-based model-checking techniques implemented in two tools: PRISM and MRMC. We show that for several models these existing tools fail to compute the result, while the two-phase method successfully computes the result efficiently with respect to time and space.