The complexity of probabilistic verification
Journal of the ACM (JACM)
Temporal Logics for the Specification of Performance and Reliability
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Computing Minimum and Maximum Reachability Times in Probabilistic Systems
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
How to Specify and Verify the Long-Run Average Behavior of Probabilistic Systems
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
The complexity of solving reachability games using value and strategy iteration
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Model checking durational probabilistic systems
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Stochastic model checking with stochastic comparison
EPEW'05/WS-FM'05 Proceedings of the 2005 international conference on European Performance Engineering, and Web Services and Formal Methods, international conference on Formal Techniques for Computer Systems and Business Processes
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Probabilistic model checking mainly concentrates on techniques for reasoning about the probabilities of certain path properties or expected values of certain random variables. For the quantitative system analysis, however, there is also another type of interesting performance measure, namely quantiles. A typical quantile query takes as input a lower probability bound p∈]0,1] and a reachability property. The task is then to compute the minimal reward bound r such that with probability at least p the target set will be reached before the accumulated reward exceeds r. Quantiles are well-known from mathematical statistics, but to the best of our knowledge they have not been addressed by the model checking community so far. In this paper, we study the complexity of quantile queries for until properties in discrete-time finite-state Markov decision processes with nonnegative rewards on states. We show that qualitative quantile queries can be evaluated in polynomial time and present an exponential algorithm for the evaluation of quantitative quantile queries. For the special case of Markov chains, we show that quantitative quantile queries can be evaluated in pseudo-polynomial time.