Abstract
General methods have been proposed [2,4] for the model checking of probabilistic systems, where the verification of a probabilistic statement is reduced to the solution of a linear system over the system’s state space. To overcome the state space explosion problem, some probabilistic model checkers, such as PRISM [3], use MTBDDs. We propose a different solution, in which we use a Monte-Carlo algorithm [6] to approximate Prob[ψ], the probability that a temporal formula is true. We show how to obtain a randomized estimator of Prob[ψ] for a fragment of LTL formulas. This fragment is sufficient to express interesting properties such as reachability and liveness.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
A. Biere, A. Cimatti, E. Clarke, and Y. Zhu. Symbolic model checking without BDD’s. Proc. of 5th TACAS, LNCS 1573:193–207, 1999.
C. Courcoubetis and M. Yannakakis. The complexity of probabilistic verification. Journal of the ACM, 42(4):857–907, 1995.
L. de Alfaro, M. Kwiatkowska, G. Norman, D. Parker, and R. Segala. Symbolic model checking of concurrent probabilistic processes using MTBDDs and the Kronecker representation. In Proc. of TACAS, LNCS 1785, 2000.
H. Hansson and B. Jonsson. A logic for reasoning about time and reliability. Formal Aspects of Computing, 6:512–535, 1994.
A. Itai and M. Rodeh. Symmetry breaking in distributed networks. Information and Computation, 88(1):60–87, 1990.
R.M. Karp and M. Luby. Monte-Carlo algorithms for enumeration and reliability problems. In Proceedings of the 24th FOCS, 56–64, 1983.
R. Motwani and P. Raghavan. Randomized Algorithms. Cambridge University Press, 1995.
A. Pnueli and L. Zuck. Verification of multiprocess probabilistic protocols. Distributed Computing, pages 1:53–72, 1986.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lassaigne, R., Peyronnet, S. (2002). Approximate Verification of Probabilistic Systems. In: Hermanns, H., Segala, R. (eds) Process Algebra and Probabilistic Methods: Performance Modeling and Verification. PAPM-PROBMIV 2002. Lecture Notes in Computer Science, vol 2399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45605-8_16
Download citation
DOI: https://doi.org/10.1007/3-540-45605-8_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43913-4
Online ISBN: 978-3-540-45605-6
eBook Packages: Springer Book Archive