Abstract
For verification and performance evaluation, system models that can express stochastic as well as real-time behaviour are of increasing importance. Although an integrated stochastic-timed verification procedure is highly desirable, both model-checking and simulation currently fall short of providing a complete, fully automatic verification solution. For model-checking, the problem lies in the extreme expressiveness of such a model, while simulation is limited to stochastic processes and cannot deal with nondeterminism. In this paper, we review the use of stochastic timed automata as an overarching formalism to model stochastic timed systems and present two analysis approaches: Model-checking for the (large) subset corresponding to probabilistic timed automata with deadlines, for which solid implementations are appearing, and simulation, which we have recently shown to be applicable to models that also include spurious nondeterministic choices.
This work has been supported by the by the EU FP7 under grant number ICT-214755 (Quasimodo), by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS) and by the DFG/NWO Bilateral Research Programme ROCKS.
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References
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Baier, C., D’Argenio, P.R., Größer, M.: Partial order reduction for probabilistic branching time. Electr. Notes Theor. Comput. Sci. 153(2), 97–116 (2006)
Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.P.: Performance evaluation and model checking join forces. Commun. ACM 53(9), 76–85 (2010)
Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)
Basu, A., Bensalem, S., Bozga, M., Caillaud, B., Delahaye, B., Legay, A.: Statistical abstraction and model-checking of large heterogeneous systems. In: Hatcliff, J., Zucca, E. (eds.) FMOODS/FORTE 2010. LNCS, vol. 6117, pp. 32–46. Springer, Heidelberg (2010)
Bogdoll, J., Ferrer Fioriti, L.M., Hartmanns, A., Hermanns, H.: Partial order methods for statistical model checking and simulation. In: Bruni, R., Dingel, J. (eds.) FMOODS/FORTE 2011. LNCS, vol. 6722, pp. 59–74. Springer, Heidelberg (2011)
Bohnenkamp, H.C., D’Argenio, P.R., Hermanns, H., Katoen, J.P.: MoDeST: A compositional modeling formalism for hard and softly timed systems. IEEE Transactions on Software Engineering 32(10), 812–830 (2006)
Bornot, S., Sifakis, J.: An algebraic framework for urgency. Inf. Comput. 163(1), 172–202 (2000)
Cavin, D., Sasson, Y., Schiper, A.: On the accuracy of MANET simulators. In: POMC, pp. 38–43. ACM, New York (2002)
Daws, C., Kwiatkowska, M.Z., Norman, G.: Automatic verification of the IEEE 1394 root contention protocol with KRONOS and PRISM. STTT 5(2-3), 221–236 (2004)
Eisentraut, C., Hermanns, H., Zhang, L.: On probabilistic automata in continuous time. In: LICS, pp. 342–351. IEEE Computer Society, Los Alamitos (2010)
Glynn, P.W.: A GSMP formalism for discrete event systems. Proceedings of the IEEE 77, 14–23 (1989)
Godefroid, P.: Partial-Order Methods for the Verification of Concurrent Systems – An Approach to the State-Explosion Problem. LNCS, vol. 1032. Springer, Heidelberg (1996)
Gómez, R.: A compositional translation of timed automata with deadlines to uppaal timed automata. In: Ouaknine, Vaandrager (eds.) [23], pp. 179–194
Grimmet, G., Stirzaker, D.: Probability and Random Processes, 3rd edn. Oxford University Press, Oxford (2001)
Hartmanns, A., Hermanns, H.: A Modest approach to checking probabilistic timed automata. In: QEST, pp. 187–196. IEEE Computer Society, Los Alamitos (2009)
Hermanns, H.: Interactive Markov Chains: The Quest for Quantified Quality. LNCS, vol. 2428. Springer, Heidelberg (2002)
Kwiatkowska, M.Z., Norman, G., Parker, D.: Stochastic games for verification of probabilistic timed automata. In: Ouaknine, Vaandrager (eds.) [23], pp. 212–227
Kwiatkowska, M.Z., Norman, G., Parker, D., Sproston, J.: Performance analysis of probabilistic timed automata using digital clocks. Formal Methods in System Design 29(1), 33–78 (2006)
Kwiatkowska, M.Z., Norman, G., Segala, R., Sproston, J.: Automatic verification of real-time systems with discrete probability distributions. Theor. Comput. Sci. 282(1), 101–150 (2002)
Kwiatkowska, M.Z., Norman, G., Sproston, J., Wang, F.: Symbolic model checking for probabilistic timed automata. Inf. Comput. 205(7), 1027–1077 (2007)
Minea, M.: Partial order reduction for model checking of timed automata. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 431–446. Springer, Heidelberg (1999)
Ouaknine, J., Vaandrager, F.W. (eds.): FORMATS 2009. LNCS, vol. 5813. Springer, Heidelberg (2009)
Parker, D.: Implementation of Symbolic Model Checking for Probabilistic Systems. Ph.D. thesis, University of Birmingham (2002)
Peled, D.: Combining partial order reductions with on-the-fly model-checking. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 377–390. Springer, Heidelberg (1994)
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons Inc., New York (1994)
Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. Ph.D. thesis, MIT, Cambridge, MA, USA (1995)
Valmari, A.: A stubborn attack on state explosion. In: Clarke, E.M., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 156–165. Springer, Heidelberg (1991)
Younes, H.L.S., Kwiatkowska, M.Z., Norman, G., Parker, D.: Numerical vs. Statistical probabilistic model checking: An empirical study. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 46–60. Springer, Heidelberg (2004)
Younes, H.L.S., Simmons, R.G.: Probabilistic verification of discrete event systems using acceptance sampling. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 223–235. Springer, Heidelberg (2002)
Zhang, L., Neuhäußer, M.R.: Model checking interactive markov chains. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 53–68. Springer, Heidelberg (2010)
Zuliani, P., Platzer, A., Clarke, E.M.: Bayesian statistical model checking with application to simulink/stateflow verification. In: Johansson, K.H., Yi, W. (eds.) HSCC, pp. 243–252. ACM, New York (2010)
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Hartmanns, A. (2011). Model-Checking and Simulation for Stochastic Timed Systems. In: Aichernig, B.K., de Boer, F.S., Bonsangue, M.M. (eds) Formal Methods for Components and Objects. FMCO 2010. Lecture Notes in Computer Science, vol 6957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25271-6_20
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DOI: https://doi.org/10.1007/978-3-642-25271-6_20
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