Using Stochastic Comparison for Efficient Model Checking of Uncertain Markov Chains

• Authors: Serge Haddad;Nihal Pekergin
• Venue: QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
• Year: 2009

We consider model checking of Discrete Time Markov Chains(DTMC) with transition probabilities which are not exactly known butlie in a given interval. Model checking a Probabilistic Computation Tree Logic (PCTL)formula for interval-valued DTMCs (IMC) has been shown to be NP hard and co-NP hard.Since the state space of a realistic DTMC is generally huge, these lower bounds preventthe application of exact algorithms for such models. Therefore we propose to apply the stochastic comparison method tocheckan extended version of PCTLfor IMCs. More precisely, we first designlinear timealgorithms to quantitatively analyzeIMCs. Then we developan efficient,semi-decidable PCTL model checking procedure for IMCs. Furthermore, our procedure returns more refinedanswers than traditional ones: \emph{YES, NO, DON'T KNOW}. Thus we may provide useful partial information for modelers in the`DON'T KNOW' case.