Abstract
A major obstacle for using partial order reduction in the context of real time verification is that the presence of clocks and clock constraints breaks the usual diamond structure of otherwise independent transitions. This is especially true when information of the relative values of clocks is preserved in the form of diagonal constraints. However, when diagonal constraints are relaxed by a suitable abstraction, some diamond structure is re-introduced in the zone graph. In this article, we introduce a variant of the stubborn set method for reducing an abstracted zone graph. Our method works with all abstractions, but especially targets situations where one abstract execution can simulate several permutations of the corresponding concrete execution, even though it might not be able to simulate the permutations of the abstract execution. We define independence relations that capture this “hidden” diamond structure, and define stubborn sets using these relations. We provide a reference implementation for verifying timed language inclusion, to demonstrate the effectiveness of our method.
Chapter PDF
Similar content being viewed by others
References
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Alur, R., Itai, A., Kurshan, R.P., Yannakakis, M.: Timing verification by successive approximation. Inf. Comput. 118(1), 142–157 (1995)
Behrmann, G., Bouyer, P., Larsen, K., Pelanek, R.: Lower and upper bounds in zone-based abstractions of timed automata. International Journal on Software Tools for Technology Transfer (STTT) 8, 204–215 (2006)
Bengtsson, J., Jonsson, B., Lilius, J., Yi, W.: Partial order reductions for timed systems. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 485–500. Springer, Heidelberg (1998)
Dams, D., Gerth, R., Knaack, B., Kuiper, R.: Partial-order reduction techniques for real-time model checking. Formal Aspects of Computing 10, 469–482 (1998)
Daws, C., Tripakis, S.: Model checking of real-time reachability properties using abstractions. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 313–329. Springer, Heidelberg (1998)
Evangelista, S., Pajault, C.: Solving the ignoring problem for partial order reduction. International Journal on Software Tools for Technology Transfer 12(2), 155–170 (2010)
Hansen, H., Kwiatkowska, M., Qu, H.: Partial order reduction for model checking markov decision processes under unconditional fairness. In: QEST 2011, pp. 203–212. IEEE CS Press (2011)
Hansen, H., Wang, X.: Compositional analysis for weak stubborn sets. In: Caillaud, K.H.B., Carmona, J. (eds.) Proceedings of ACSD 2011, pp. 36–43. IEEE CS Press (2011)
Herbreteau, F., Srivathsan, B., Walukiewicz, I.: Better Abstractions for Timed Automata. In: LICS, pp. 375–384 (2012)
Lugiez, D., Niebert, P., Zennou, S.: A partial order semantics approach to the clock explosion problem of timed automata. Theoretical Computer Science 345(1), 27–59 (2005)
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)
Niebert, P., Qu, H.: Adding invariants to event zone automata. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 290–305. Springer, Heidelberg (2006)
Salah, R., Bozga, M., Maler, O.: On interleaving in timed automata. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 465–476. Springer, Heidelberg (2006)
Sun, J., Liu, Y., Dong, J.S., Pang, J.: PAT: Towards Flexible Verification under Fairness. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 709–714. Springer, Heidelberg (2009)
Valmari, A.: A stubborn attack on state explosion. Formal Methods in System Design 1(1), 297–322 (1992)
Valmari, A.: Stubborn set methods for process algebras. In: Proceedings of the DIMACS Workshop on Partial Order Methods in Verification, POMIV 1996, pp. 213–231. AMS Press, Inc., New York (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Hansen, H., Lin, SW., Liu, Y., Nguyen, T.K., Sun, J. (2014). Diamonds Are a Girl’s Best Friend: Partial Order Reduction for Timed Automata with Abstractions. In: Biere, A., Bloem, R. (eds) Computer Aided Verification. CAV 2014. Lecture Notes in Computer Science, vol 8559. Springer, Cham. https://doi.org/10.1007/978-3-319-08867-9_26
Download citation
DOI: https://doi.org/10.1007/978-3-319-08867-9_26
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08866-2
Online ISBN: 978-3-319-08867-9
eBook Packages: Computer ScienceComputer Science (R0)