Abstract
We report on a novel development to model check quantitative reachability properties on Markov decision processes together with its prototype implementation. The innovation of the technique is that the analysis is performed on an abstraction of the model under analysis. Such an abstraction is significantly smaller than the original model and may safely refute or accept the required property. Otherwise, the abstraction is refined and the process repeated. As the numerical analysis necessary to determine the validity of the property is more costly than the refinement process, the technique profits from applying such numerical analysis on smaller state spaces.
Supported by the STW-PROGRESS project TES-4999
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References
R. Alur, C. Courcoubetis, N. Halbwachs, D. Dill, and H. Wong-Toi. Minimization of timed transition systems. In R. Cleaveland, ed., Procs. of CONCUR 92, Stony Brook, NY, LNCS 630, pp. 340–354. Springer, 1992.
A. Aziz, V. Singhal, F. Balarin, R.K. Bryton, and A.L. Sangiovanni-Vincentelli. It usually works:the temporal logics of stochastic systems. In P. Wolper, ed., Procs. of the 7th CAV, Liège, LNCS 939, pp. 155–165. Springer, 1995.
R.I. Bahar, E.A. Frohm, C.M. Gaona, G.D. Hachtel, E. Macii, A. Pardo, and F. Somenzi. Algebraic decision diagrams and their applications. Formal Methods in System Design, 10(2/3):171–206, 1997.
C. Baier, J.-P. Katoen, and H. Hermanns. Approximate symbolic model checking of continuous-time Markov chains. In J.C.M. Baeten and S. Mauw, eds., Procs. of CONCUR 99, Eindhoven, LNCS 1664, pp. 146–161. Springer, 1999.
A. Bianco and L. de Alfaro. Model checking of probabilistic and non-deterministic systems. In Procs. 15 th FSTTCS, Pune, LNCS 1026, pp. 499–513. Springer, 1995.
A. Bouajjani, J. C. Fernandez, N. Halbwachs, P. Raymond, and C. Ratel. Minimal state graph generation. Science of Computer Programming, 18:247–269, 1992.
P.R. D’Argenio, J.-P. Katoen, T.C. Ruys, and J. Tretmans. The bounded retransmission protocol must be on time! In E. Brinksma, ed., Procs. of the 3rd TACAS, Enschede, LNCS 1217, pp. 416–431. Springer, 1997.
P.R. D’Argenio, B. Jeannet, H.E. Jensen, and K.G. Larsen. Reachability Analysis of Probabilistic Systems by Successive Refinements. CTIT Technical Report, 2001. To appear.
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 Graf and Schwartzbach [11].
M. Fujita, P.C. McGeer, and J.C.-Y. Yang. Multi-terminal binary decision diagrams: An efficient data structure for matrix representation. Formal Methods in System Design, 10(2/3):149–169, April 1997.
S. Graf and M. Schwartzbach, eds. Procs. of the 6th Workshop TACAS, Berlin, LNCS 1785. Springer, 2000.
J.F. Groote and J. van de Pol. A bounded retransmission protocol for large data packets — A case study in computer checked algebraic verification. In M. Wirsing and M. Nivat, eds., Procs. of the 5 th AMAST Conference, Munich, LNCS 1101. Springer, 1996.
H.A. Hansson and B. Jonsson. A logic for reasoning about time and reliability. Formal Aspects of Computing, 6:512–535, 1994.
V. Hartonas-Garmhausen and S. Campos. ProbVerus: Probabilistic symbolic model mhecking. In In Katoen [24], pp. 96–110.
L. Helmink, M.P.A. Sellink, and F.W. Vaandrager. Proof-checking a data link protocol. In H. Barendregt and T. Nipkow, eds., Procs. International Workshop TYPES’93, Nijmegen, LNCS 806, pp. 127–165. Springer, 1994.
H. Hermanns. Personal communication, 2001.
H. Hermanns, J.-P. Katoen, J. Meyer-Kayser, and M. Siegle. A Markov chain model checker. In Graf and Schwartzbach [11], p. 347–362.
H. Hermanns, J. Meyer-Kayser, and M. Siegle. Multi terminal binary decision diagrams to represent and analyse continuous time Markov chains. In B. Plateau, W.J. Stewart, and M. Silva, eds., 3rd Int. Workshop on the Numerical Solution of Markov Chains, pp. 188–207. Prensas Universitarias de Zaragoza, 1999.
C.A.R. Hoare. Communicating Sequential Processes. Prentice-Hall International, Englewood Cliffs, 1985.
M. Huth and M. Kwiatkowska. Quantitative analysis and model checking. In Procs. 12 th Annual Symposium on Logic in Computer Science, Warsaw. IEEE Press, 1997.
B. Jeannet. Dynamic partitioning in linear relation analysis. Application to the verification of reactive systems. Formal Methods in System Design, 2001. To appear.
B. Jonsson and K.G. Larsen. Specification and refinement of probailistic processes. In Procs. 6 th Annual Symposium on Logic in Computer Science, Amsterdam, pp. 266–277. IEEE Press, 1991.
B. Jonsson, K.G. Larsen, and W. Yi. Probabilistic extensions in process algebras. In J.A. Bergstra, A. Ponse, and S. Smolka, eds., Handbook of Process Algebras, pp. 685–710. Elsevier, 2001.
J.-P. Katoen, ed. Procs of the 5th ARTS, Bamberg, LNCS 1601. Springer, 1999.
M. Kwiatkowska, G. Norman, R. Segala, and J. Sproston. Automatic verification of real-time systems with probability distributions. In Katoen [24], pp. 75–95.
K.G. Larsen and A. Skou. Bisimulation through probabilistic testing. Information and Computation, 94:1–28, 1991.
M.L. Puterman. Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons, 1994.
R. Segala. Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Massachusetts Institute of Technology, 1995.
H. Sipma, T.E. Uribe, and Z. Manna. Deductive model checking. In R. Alur and T.A. Henzinger, eds. Procs. of the 8th CAV, New Brunswick, New Jersey, LNCS 1102. Springer, 1996.
F. Somenzi. Cudd: Colorado University Decision Diagram Package. ftp://vlsi.colorado.edu/pub.
R. F. Lutje Spelberg, W. J. Toetenel, and M. Ammerlaan. Partition refinement in real-time model checking. In A.P. Ravn and H. Rischel, eds., Procs. of the 5th FTRTFT, Lyngby, LNCS 1486, pp. 143–157. Springer, 1998.
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D’Argenio, P.R., Jeannet, B., Jensen, H.E., Larsen, K.G. (2001). Reachability Analysis of Probabilistic Systems by Successive Refinements. In: de Alfaro, L., Gilmore, S. (eds) Process Algebra and Probabilistic Methods. Performance Modelling and Verification. PAPM-PROBMIV 2001. Lecture Notes in Computer Science, vol 2165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44804-7_3
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