Bounded Model Checking for GSMP Models of Stochastic Real-Time Systems
Model checking is a popular algorithmic verification technique for checking temporal requirements of mathematical models of systems. In this paper, we consider the problem of verifying bounded reachability properties of stochastic real-time systems modeled as generalized semi-Markov processes (GSMP). While GSMPs is a rich model for stochastic systems widely used in performance evaluation, existing model checking algorithms are applicable only to subclasses such as discrete-time or continuous-time Markov chains. The main contribution of the paper is an algorithm to compute the probability that a given GSMP satisfies a property of the form “can the system reach a target before time T within k discrete events, while staying within a set of safe states”. For this, we show that the probability density function for the remaining firing times of different events in a GSMP after k discrete events can be effectively partitioned into finitely many regions and represented by exponentials and polynomials. We report on illustrative examples and their analysis using our techniques.
KeywordsModel Check Mass Point Destination Location Discrete Event System Symbolic Model Check
Unable to display preview. Download preview PDF.
- 4.Biere, A., Cimatti, A., Clarke, E., Fujita, M., Zhu, Y.: Symbolic model checking using SAT procedures instead of BDDs. In: Proceedings of the 36th ACM/IEEE Design Automation Conference, pp. 317–320 (1999)Google Scholar
- 5.Clarke, E.M., Grumberg, O., Peled, D.A.: Model checking. MIT Press, Cambridge (2000)Google Scholar
- 10.Hansson, H., Jonsson, B.: A framework for reasoning about time and reliability. In: Proceedings of the Tenth IEEE Real-Time Systems Symposium, pp. 102–111 (1989)Google Scholar
- 13.Kwiatkowska, M., Norman, G., Parker, D.: PRISM: Probabilistic symbolic model checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 200–204. Springer, Heidelberg (2002)Google Scholar
- 15.Kwiatkowska, M.Z.: Model checking for probability and time: from theory to pratice. In: Proceedings of the 18th IEEE Symposium on Logic in Computer Science, pp. 351–360 (2003)Google Scholar
- 19.Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state programs. In: Proceedings of the 26th IEEE Symposium on Foundations of Computer Science, pp. 327–338 (1985)Google Scholar