Abstract
Quantitative analysis of probabilistic systems has been studied mainly from the global model checking point of view. In the global model-checking, the goal of verification is to decide the probability of satisfaction of a given property for all reachable states in the state space of the system under investigation. On the other hand, in local model checking approach the probability of satisfaction is computed only for the set of initial states. In theory, it is possible to solve the local model checking problem using the global model checking approach. However, the global model checking procedure can be significantly outperformed by a dedicated local model checking one. In this paper we present several particular local model checking techniques that if applied to global model checking procedure reduce the runtime needed from days to minutes.
This work has been partially supported by the Grant Agency of Czech Republic grant No. 201/06/1338 and the Academy of Sciences grant No. 1ET408050503.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.K.: Verifying continuous-time Markov Chains. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 269–276. Springer, Heidelberg (1996)
Aspnes, J., Herlihy, M.: Fast randomized consensus using shared memory. Journal of Algorithms 15(1), 441–460 (1990)
Baier, C.: On the Algorithmic Verification of Probabilistic Systems. Habilitation Thesis, Universität Mannheim (1998)
Baier, C., Größer, M., Ciesinski, F.: Partial Order Reduction for Probabilistic Systems. In: 1st International Conference on Quantitative Evaluation of Systems (QEST 2004), pp. 230–239. IEEE Computer Society, Los Alamitos (2004)
Barnat, J., Brim, L., Černá, I., Češka, M., Tůmová, J.: ProbDiVinE-MC: Multi-Core LTL Model Checker for Probabilistic Systems. In: Proceedings of QEST 2008, Tool Paper. IEEE, Los Alamitos (2008) (to appear), http://anna.fi.muni.cz/probdivine
Barnat, J., Chaloupka, J., van de Pol, J.: Improved Distributed Algorithms for SCC Decomposition. Electron. Notes Theor. Comput. Sci. 198(1), 63–77 (2008)
Bianco, A., de Alfaro, L.: Model checking of probabilistic and nondeterministic systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995)
Jeannet, B., de Argenio, P., Larsen, K.G.: RAPTURE: A tool for verifying Markov Decision Processes. In: Proc. Tools Day / CONCUR 2002. Tech. Rep. FIMU-RS-2002-05. MU Brno, pp. 84–98 (2002)
Chaum, D.: The dining cryptographers problem: Unconditional sender and recipient untraceability. Journal of Cryptology 1, 65–75 (1988)
Ciesinski, F., Baier, C.: LiQuor: A tool for Qualitative and Quantitative Linear Time analysis of Reactive Systems. In: Proc. of QEST 2006, pp. 131–132. IEEE Computer Society, Los Alamitos (2006)
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)
de Alfaro, L.: Formal Verification of Stochastic Systems. PhD thesis, Stanford University, Department of Computer Science (1997)
Derman, C.: Finite State Markovian Decision Processes. Academic Press, Inc., Orlando (1970)
Doob, J.L.: Measure theory. Springer, Heidelberg (1994)
Hansson, H., Jonsson, B.: A Framework for Reasoning about Time and Reliability. In: IEEE Real-Time Systems Symposium, pp. 102–111 (1989)
Hinton, A., Kwiatkowska, M., Norman, G., Parker, D.: PRISM: A tool for automatic verification of probabilistic systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006)
Israeli, A., Jalfon, M.: Token management schemes and random walks yield self-stabilizating mutual exclusion. In: Proc. ACM Symposium on Principles of Distributed Computing, pp. 119–131 (1990)
Itai, A., Rodeh, M.: Symmetry breaking in distributed networks. Information and Computation 88(1) (1990)
Lehmann, D., Rabin, M.: On the advantage of free choice: A symmetric and fully distributed solution to the dining philosophers problem (extended abstract). In: Proc. 8th Annual ACM Symposium on Principles of Programming Languages (POPL 1981), pp. 133–138 (1981)
ProbDiVinE homepage (2008), http://anna.fi.muni.cz/probdivine
Puterman, M.L.: Markov Decision Processes-Discrete Stochastic Dynamic Programming. John Wiley &Sons, New York (1994)
Vardi, M.Y.: Probabilistic linear-time model checking: an overview of the automata-theoretic approach. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 265–276. Springer, Heidelberg (1999)
Vardi, M.Y., Wolper, P.: Reasoning about infinite computation paths. In: Proceedings of 24th IEEE Symposium on Foundation of Computer Science, Tuscan, pp. 185–194 (1983)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Barnat, J., Brim, L., Černá, I., Češka, M., Tůmová, J. (2009). Local Quantitative LTL Model Checking . In: Cofer, D., Fantechi, A. (eds) Formal Methods for Industrial Critical Systems. FMICS 2008. Lecture Notes in Computer Science, vol 5596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03240-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-03240-0_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03239-4
Online ISBN: 978-3-642-03240-0
eBook Packages: Computer ScienceComputer Science (R0)