Abstract
In this paper, we introduce a new approach to computing abstractions for hybrid dynamical systems whose continuous behavior is governed by non-linear ordinary differential equations. The abstractions try to capture the reachability information relevant for a given safety property as succinctly as possible. This is achieved by an incremental refinement of the abstractions, simultaneously trying to avoid increases in their size as much as possible. The approach is independent of a concrete technique for computing reachability information, and can hence be combined with whatever technique suitable for the problem class at hand. We illustrate the usefulness of the technique with computational experiments.
This work was supported by Czech Science Foundation grants 201/08/J020 and 201/09/H057, MŠMT project number OC10048 and institutional research plan AV0Z100300504.
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References
Alur, R., Dang, T., Ivančić, F.: Predicate abstraction for reachability analysis of hybrid systems. Trans. on Embedded Computing Sys. 5(1), 152–199 (2006)
Apt, K.R.: The essence of constraint propagation. Theoretical Computer Science 221(1–2), 179–210 (1999)
Apt, K.R.: The role of commutativity in constraint propagation algorithms. ACM Transactions on Programming Languages and Systems 22(6), 1002–1036 (2000)
Benhamou, F., Granvilliers, L.: Continuous and interval constraints. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming. ch.16, pp. 571–603. Elsevier, Amsterdam (2006)
Bourdoncle, F.: Efficient chaotic iteration strategies with widenings. In: Bjørner, D., Broy, M., Pottosin, I. (eds.) FMP&TA 1993. LNCS, vol. 735, pp. 128–141. Springer, Heidelberg (1993)
Brückner, I., Dräger, K., Finkbeiner, B., Wehrheim, H.: Slicing abstractions. Fundamenta Informaticae 89(4), 369–392 (2008)
Clarke, E., Fehnker, A., Han, Z., Krogh, B., Ouaknine, J., Stursberg, O., Theobald, M.: Abstraction and counterexample-guided refinement in model checking of hybrid systems. Int. J. of Foundations of Comp. Sc. 14(4), 583–604 (2003)
Cousot, P., Cousot, R.: Automatic synthesis of optimal invariant assertions: Mathematical foundations. In: Proceedings of the 1977 Symposium on Artificial Intelligence and Programming Languages, pp. 1–12 (1977)
Damm, W., Pinto, G., Ratschan, S.: Guaranteed termination in the verification of LTL properties of non-linear robust discrete time hybrid systems. International Journal of Foundations of Computer Science (IJFCS) 18(1), 63–86 (2007)
Dzetkulič, T., Ratschan, S.: How to capture hybrid systems evolution into slices of parallel hyperplanes. In: ADHS 2009: 3rd IFAC Conference on Analysis and Design of Hybrid Systems, pp. 274–279 (2009)
Frehse, G., Krogh, B.H., Rutenbar, R.A.: Verifying analog oscillator circuits using forward/backward abstraction refinement. In: DATE 2006: Design, Automation and Test in Europe (2006)
Henzinger, T.A., Ho, P.-H.: A note on abstract interpretation strategies for hybrid automata. LNCS, vol. 999, pp. 252–264 (1995)
Nielson, F., Nielson, H.R., Hankin, C.: Principles of Program Analysis. Springer, Heidelberg (1999)
Ratschan, S.: Efficient solving of quantified inequality constraints over the real numbers. ACM Transactions on Computational Logic 7(4), 723–748 (2006)
Ratschan, S.: Safety verification of non-linear hybrid systems is quasi-semidecidable. In: Kratochvíl, J., Li, A., Fiala, J., Kolman, P. (eds.) TAMC 2010. LNCS, vol. 6108, pp. 397–408. Springer, Heidelberg (2010)
Ratschan, S., She, Z.: Safety verification of hybrid systems by constraint propagation based abstraction refinement. ACM Transactions in Embedded Computing Systems 6(1) (2007)
Ratschan, S., Smaus, J.-G.: Finding errors of hybrid systems by optimising an abstraction-based quality estimate. In: Dubois, C. (ed.) TAP 2009. LNCS, vol. 5668, pp. 153–168. Springer, Heidelberg (2009)
Tiwari, A., Gulwani, S.: Logical interpretation: Static program analysis using theorem proving. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 147–166. Springer, Heidelberg (2007)
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Dzetkulič, T., Ratschan, S. (2011). Incremental Computation of Succinct Abstractions for Hybrid Systems. In: Fahrenberg, U., Tripakis, S. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2011. Lecture Notes in Computer Science, vol 6919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24310-3_19
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DOI: https://doi.org/10.1007/978-3-642-24310-3_19
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