Guaranteed Termination in the Verification of LTL Properties of Non-linear Robust Discrete Time Hybrid Systems

  • Werner Damm
  • Guilherme Pinto
  • Stefan Ratschan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3707)


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.


Model Check Hybrid System Transition System Interval Arithmetic Safety Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Henzinger, T.A., Sastry, S.S. (eds.): HSCC 1998. LNCS, vol. 1386. Springer, Heidelberg (1998)MATHGoogle Scholar
  12. 12.
    Neumaier, A.: Interval Methods for Systems of Equations. Cambridge Univ. Press, Cambridge (1990)MATHGoogle Scholar
  13. 13.
    Ratschan, S.: Quantified constraints under perturbations. Journal of Symbolic Computation 33(4), 493–505 (2002)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Ratschan, S.: Rsolver. Software package (2004),
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    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)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Werner Damm
    • 1
  • Guilherme Pinto
    • 1
  • Stefan Ratschan
    • 2
  1. 1.Carl v. Ossietzky UniversitätOldenburgGermany
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

Personalised recommendations