Abstract
Monte Carlo model checking introduced by Smolka and Grosu is an approach to analyse non-probabilistic models using sampling and draw conclusions with a given confidence interval by applying statistical inference. Though not exhaustive, the method enables verification of complex models, even in cases where the underlying problem is undecidable. In this paper we develop Monte Carlo model checking techniques to evaluate quantitative properties of timed languages. Our approach is based on uniform random sampling of behaviours, as opposed to isotropic sampling that chooses the next step uniformly at random. The uniformity is defined with respect to volume measure of timed languages previously studied by Asarin, Basset and Degorre. We improve over their work by employing a zone graph abstraction instead of the region graph abstraction and incorporating uniform sampling within a zone-based Monte Carlo model checking framework. We implement our algorithms using tools PRISM, SageMath and COSMOS, and demonstrate their usefulness on statistical language inclusion measurement in terms of volume.
This work is supported by ERC AdG VERIWARE.
B. Barbot—Now in LACL, Université Paris Est Créteil, France
M. Beunardeau—Contributed to the work during an internship funded by ERC AdG VERIWARE.
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Notes
- 1.
Our approach to timed languages is based on volume and does not apply, in its present form, to unbounded delays that result in innite volume.
- 2.
Note that some works, consider instead sampling the delay first and then the transitions available in the state updated by the delay (see [9]).
References
Alur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126, 183–235 (1994)
Asarin, E., Basset, N., Béal, M.-P., Degorre, A., Perrin, D.: Toward a timed theory of channel coding. In: Jurdziński, M., Ničković, D. (eds.) FORMATS 2012. LNCS, vol. 7595, pp. 27–42. Springer, Heidelberg (2012)
Asarin, E., Basset, N., Degorre, A.: Entropy of regular timed languages. Inf. Comput. 241, 142–176 (2015)
Ballarini, P., Barbot, B., Duflot, M., Haddad, S., Pekergin, N.: HASL: a new approach for performance evaluation and model checking from concepts to experimentation. Perform. Eval. 90, 53–77 (2015)
Barbot, B., Basset, N., Beunardeau, M., Kwiatkowska, M.: Uniform sampling for timed automata with application to language inclusion measurement. Technical report CS-RR-16-04, University of Oxford (2016)
Basset, N.: Counting and generating permutations using timed languages. In: Pardo, A., Viola, A. (eds.) LATIN 2014. LNCS, vol. 8392, pp. 502–513. Springer, Heidelberg (2014)
Basset, N.: A maximal entropy stochastic process for a timed automaton. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 61–73. Springer, Heidelberg (2013)
Bengtsson, J.E., Yi, W.: Timed automata: semantics, algorithms and tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) Lectures on Concurrency and Petri Nets. LNCS, vol. 3098, pp. 87–124. Springer, Heidelberg (2004)
Bohlender, D., Bruintjes, H., Junges, S., Katelaan, J., Nguyen, V.Y., Noll, T.: A review of statistical model checking pitfalls on real-time stochastic models. In: Margaria, T., Steffen, B. (eds.) ISoLA 2014, Part II. LNCS, vol. 8803, pp. 177–192. Springer, Heidelberg (2014)
David, A., Larsen, K.G., Legay, A., Mikucionis, M., Poulsen, D.B.: UPPAAL SMC tutorial. STTT 17(4), 397–415 (2015)
Denise, A., Gaudel, M.-C., Gouraud, S.-D., Lassaigne, R., Oudinet, J., Peyronnet, S.: Coverage-biased random exploration of large models and application to testing. STTT 14(1), 73–93 (2012)
Flajolet, P., Zimmerman, P., Van Cutsem, B.: A calculus for the random generation of labelled combinatorial structures. Theoret. Comput. Sci. 132(1), 1–35 (1994)
Grosu, R., Smolka, S.A.: Monte Carlo model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 271–286. Springer, Heidelberg (2005)
Henzinger, T.A., Raskin, J.-F.: Robust undecidability of timed and hybrid systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 145–159. Springer, Heidelberg (2000)
Jaynes, E.T.: Information theory and statistical mechanics II. Phys. Rev. Online Arch. (PROLA) 108(2), 171–190 (1957)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011)
Murray, R.M., Hauser, J., Jadbabaie, A., Milam, M.B., Petit, N., Dunbar, W.B., Franz, R.: Online control customization via optimization-based control. In: Software-Enabled Control: Information Technology for Dynamical Systems, p. 149 (2003)
Oualhadj, Y., Reynier, P.-A., Sankur, O.: Probabilistic robust timed games. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 203–217. Springer, Heidelberg (2014)
Oudinet, J., Denise, A., Gaudel, M.-C., Lassaigne, R., Peyronnet, S.: Uniform monte-carlo model checking. In: Giannakopoulou, D., Orejas, F. (eds.) FASE 2011. LNCS, vol. 6603, pp. 127–140. Springer, Heidelberg (2011)
Stein, W.A., et al.: Sage Mathematics Software (Version 6.9). The Sage Development Team (2015). http://www.sagemath.org
Younes, H.L.S., Simmons, R.G.: Statistical probabilistic model checking with a focus on time-bounded properties. Inf. Comput. 204(9), 1368–1409 (2006)
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Barbot, B., Basset, N., Beunardeau, M., Kwiatkowska, M. (2016). Uniform Sampling for Timed Automata with Application to Language Inclusion Measurement. In: Agha, G., Van Houdt, B. (eds) Quantitative Evaluation of Systems. QEST 2016. Lecture Notes in Computer Science(), vol 9826. Springer, Cham. https://doi.org/10.1007/978-3-319-43425-4_13
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