Abstract
We present a novel approach to the automatic verification and falsification of LTL requirements of non-linear discrete-time hybrid systems. The verification tool uses an interval-based constraint solver for non-linear robust constraints to compute incrementally refined abstractions. Although the problem is in general undecidable, we prove termination of abstraction refinement based verification and falsification of such properties for the class of robust non-linear hybrid systems, thus significantly extending previous semi-decidability results. We argue, that safety critical control applications are robust hybrid systems. We give first results on the application of this approach to a variant of an aircraft collision avoidance protocol.
This work was partly supported 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). See www.avacs.org for more information.
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References
Asarin, E., Dang, T., Maler, O.: The d/dt tool for verification of hybrid systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 365–370. Springer, Heidelberg (2002)
Bienmüller, T., Bohn, J., Brinkmann, H., Brockmeyer, U., Damm, W., Hungar, H., Jansen, P.: Verification of automotive control units. In: Olderog, E.-R., Steffen, B. (eds.) Correct System Design. LNCS, vol. 1710, pp. 319–341. Springer, Heidelberg (1999)
Bienmüller, T., Brockmeyer, U., Damm, W.: et al. Formal verification of an avionics application using abstraction and symbolic model checking. In: Redmill, F., Anderson, T. (eds.) Towards System Safety—Proc. of the 7th Safety-critical Systems Symp., pp. 150–173. Springer, Heidelberg (1999)
Bohn, J., Damm, W., Grumberg, O., et al.: First-order-CTL model checking. In: Arvind, V., Sarukkai, S. (eds.) FST TCS 1998. LNCS, vol. 1530, pp. 283–295. Springer, Heidelberg (1998)
Chutinan, A., Krogh, B.H.: Computing polyhedral approximations to flow pipes for dynamic systems. In: 37th IEEE Conference on Decision and Control: Session on Synthesis and Verification of Hybrid Control Laws, TM-01 (1998)
Clarke, E., Fehnker, A., Han, Z., Krogh, B., Stursberg, O., Theobald, M.: Verification of hybrid systems based on counterexample-guided abstraction refinement. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 192–207. Springer, Heidelberg (2003)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)
Fränzle, M.: Analysis of hybrid systems: An ounce of realism can save an infinity of states. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 126–140. Springer, Heidelberg (1999)
Fränzle, M.: What will be eventually true of polynomial hybrid automata. In: Kobayashi, N., Pierce, B.C. (eds.) TACS 2001. LNCS, vol. 2215, p. 340. Springer, Heidelberg (2001)
Henzinger, T.A., Horowitz, B., Majumdar, R., Wong-Toi, H.: Beyond HyTech: hybrid systems analysis using interval numerical methods. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, p. 130. Springer, Heidelberg (2000)
Henzinger, T.A., Sastry, S.S. (eds.): HSCC 1998. LNCS, vol. 1386. Springer, Heidelberg (1998)
Neumaier, A.: Interval Methods for Systems of Equations. Cambridge Univ. Press, Cambridge (1990)
Ratschan, S.: Quantified constraints under perturbations. Journal of Symbolic Computation 33(4), 493–505 (2002)
Ratschan, S.: Rsolver. Software package (2004), http://rsolver.sourceforge.net
Ratschan, S., She, Z.: Safety verification of hybrid systems by constraint propagation based abstraction refinement. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 573–589. Springer, Heidelberg (2005)
Stursberg, O., Kowalewski, S., Engell, S.: On the generation of timed discrete approximations for continuous systems. Mathematical and Computer Models of Dynamical Systems 6, 51–70 (2000)
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Damm, W., Pinto, G., Ratschan, S. (2005). Guaranteed Termination in the Verification of LTL Properties of Non-linear Robust Discrete Time Hybrid Systems. In: Peled, D.A., Tsay, YK. (eds) Automated Technology for Verification and Analysis. ATVA 2005. Lecture Notes in Computer Science, vol 3707. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11562948_10
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DOI: https://doi.org/10.1007/11562948_10
Publisher Name: Springer, Berlin, Heidelberg
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