Abstract
We present an importance sampling framework that combines symbolic analysis and simulation to estimate the probability of rare reachability properties in stochastic timed automata. By means of symbolic exploration, our framework first identifies states that cannot reach the goal. A state-wise change of measure is then applied on-the-fly during simulations, ensuring that dead ends are never reached. The change of measure is guaranteed by construction to reduce the variance of the estimator with respect to crude Monte Carlo, while experimental results demonstrate that we can achieve substantial computational gains.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
One symbolic state may appear in several quadruples.
- 2.
- 3.
Details can be found at http://people.cs.aau.dk/~marius/stratego/rare.html.
References
Alur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126(2), 183–235 (1994)
Behrmann, G., Cougnard, A., David, A., Fleury, E., Larsen, K.G., Lime, D.: Uppaal-Tiga: time for playing games!. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 121–125. Springer, Heidelberg (2007). doi:10.1007/978-3-540-73368-3_14
Bulychev, P., David, A., Larsen, K.G., Legay, A., Li, G., Poulsen, D.B.: Rewrite-based statistical model checking of WMTL. In: Qadeer, S., Tasiran, S. (eds.) RV 2012. LNCS, vol. 7687, pp. 260–275. Springer, Heidelberg (2013). doi:10.1007/978-3-642-35632-2_25
Bulychev, P., David, A., Larsen, K.G., Legay, A., Li, G., Bøgsted Poulsen, D., Stainer, A.: Monitor-based statistical model checking for weighted metric temporal logic. In: Bjørner, N., Voronkov, A. (eds.) LPAR 2012. LNCS, vol. 7180, pp. 168–182. Springer, Heidelberg (2012). doi:10.1007/978-3-642-28717-6_15
Bulychev, P., David, A., Larsen, K.G., Legay, A., Mikučionis, M., Bøgsted Poulsen, D.: Checking and distributing statistical model checking. In: Goodloe, A.E., Person, S. (eds.) NFM 2012. LNCS, vol. 7226, pp. 449–463. Springer, Heidelberg (2012). doi:10.1007/978-3-642-28891-3_39
David, A., Larsen, K.G., Legay, A., Nyman, U., Wasowski, A.: Timed i/o automata: a complete specification theory for real-time systems. In: HSCC, pp. 91–100. ACM (2010)
David, A., Larsen, K.G., Legay, A., Mikučionis, M., Poulsen, D.B., Vliet, J., Wang, Z.: Statistical model checking for networks of priced timed automata. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 80–96. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24310-3_7
Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Proceedings of Automatic Verification Methods for Finite State Systems, International Workshop, Grenoble, France, June 12–14, 1989, pp. 197–212 (1989)
Jegourel, C., Legay, A., Sedwards, S.: Cross-entropy optimisation of importance sampling parameters for statistical model checking. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 327–342. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31424-7_26
Jegourel, C., Legay, A., Sedwards, S.: Importance splitting for statistical model checking rare properties. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 576–591. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39799-8_38
Kahn, H.: Use of different monte carlo sampling techniques. Technical report P-766, Rand Corporation, November 1955
Kempf, J.-F., Bozga, M., Maler, O.: Performance evaluation of schedulers in a probabilistic setting. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 1–17. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24310-3_1
Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a nutshell. STTT 1(1–2), 134–152 (1997)
Maler, O., Larsen, K.G., Krogh, B.H.: On zone-based analysis of duration probabilistic automata. In: Proceedings 12th International Workshop on Verification of Infinite-State Systems (INFINITY), pp. 33–46 (2010)
Rubino, G., Tuffin, B.: Rare Event Simulation using Monte Carlo Methods. Wiley, Hoboken (2009)
Rubinstein, R.: The cross-entropy method for combinatorial and continuous optimization. Meth. Comput. Appl. Probab. 1(2), 127–190 (1999)
Vicario, E., Sassoli, L., Carnevali, L.: Using stochastic state classes in quantitative evaluation of dense-time reactive systems. IEEE Trans. Softw. Eng. 35(5), 703–719 (2009)
Younes, H.L.S.: Verification and planning for stochastic processes with asynchronous events. Ph.D. thesis, Carnegie Mellon University (2005)
Zuliani, P., Baier, C., Clarke, E.M.: Rare-event verification for stochastic hybrid systems. In: Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control, HSCC, pp. 217–226 (2012)
Acknowledgements
This research has received funding from the Sino-Danish Basic Research Centre, IDEA4CPS, funded by the Danish National Research Foundation and the National Science Foundation, China, the Innovation Fund Denmark centre DiCyPS, as well as the ERC Advanced Grant LASSO. Other funding has been provided by the Self Energy-Supporting Autonomous Computation (SENSATION) and Collective Adaptive Systems Synthesis with Non-zero-sum Games (CASSTING) European FP7-ICT projects, and the Embedded Multi-Core systems for Mixed Criticality (EMC2) ARTEMIS project.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Jegourel, C., Larsen, K.G., Legay, A., Mikučionis, M., Poulsen, D.B., Sedwards, S. (2016). Importance Sampling for Stochastic Timed Automata. In: Fränzle, M., Kapur, D., Zhan, N. (eds) Dependable Software Engineering: Theories, Tools, and Applications. SETTA 2016. Lecture Notes in Computer Science(), vol 9984. Springer, Cham. https://doi.org/10.1007/978-3-319-47677-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-47677-3_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47676-6
Online ISBN: 978-3-319-47677-3
eBook Packages: Computer ScienceComputer Science (R0)