Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
Verifying Continuous Time Markov Chains
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Model Checking Markov Chains with Actions and State Labels
IEEE Transactions on Software Engineering
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Analysing Biochemical Oscillation through Probabilistic Model Checking
Electronic Notes in Theoretical Computer Science (ENTCS)
Model Checking Timed and Stochastic Properties with CSL^{TA}
IEEE Transactions on Software Engineering
Quantitative Model Checking of Continuous-Time Markov Chains Against Timed Automata Specifications
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
The ins and outs of the probabilistic model checker MRMC
Performance Evaluation
Automata-based CSL model checking
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
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
Automata-based CSL model checking
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Model checking conditional CSL for continuous-time Markov chains
Information Processing Letters
Approximating acceptance probabilities of CTMC-paths on multi-clock deterministic timed automata
Proceedings of the 16th international conference on Hybrid systems: computation and control
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For continuous-time Markov chains, the model-checking problem with respect to continuous-time stochastic logic (CSL) has been introduced and shown to be decidable by Aziz, Sanwal, Singhal and Brayton in 1996. The presented decision procedure, however, has exponential complexity. In this paper, we propose an effective approximation algorithm for full CSL. The key to our method is the notion of stratified CTMCs with respect to the CSL property to be checked. We present a measure-preservation theorem allowing us to reduce the problem to a transient analysis on stratified CTMCs. The corresponding probability can then be approximated in polynomial time (using uniformization). This makes the present work the centerpiece of a broadly applicable full CSL model checker. Recently, the decision algorithm by Aziz et al. was shown to be incorrect in general. In fact, it works only for stratified CTMCs. As an additional contribution, our measure-preservation theorem can be used to ensure the decidability for general CTMCs.