Inductive Verification of Hybrid Automata with Strongest Postcondition Calculus

  • Daisuke Ishii
  • Guillaume Melquiond
  • Shin Nakajima
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7940)

Abstract

Safety verification of hybrid systems is a key technique in developing embedded systems that have a strong coupling with the physical environment. We propose an automated logical analytic method for verifying a class of hybrid automata. The problems are more general than those solved by the existing model checkers: our method can verify models with symbolic parameters and nonlinear equations as well. First, we encode the execution trace of a hybrid automaton as an imperative program. Its safety property is then translated into proof obligations by strongest postcondition calculus. Finally, these logic formulas are discharged by state-of-the-art arithmetic solvers (e.g., Mathematica). Our proposed algorithm efficiently performs inductive reasoning by unrolling the execution for some steps and generating loop invariants from verification failures. Our experimental results along with examples taken from the literature show that the proposed approach is feasible.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ábrahám-Mumm, E., Steffen, M., Hannemann, U.: Verification of hybrid systems: Formalization and proof rules in PVS. In: ICECCS, pp. 48–57 (2001)Google Scholar
  2. 2.
    Abrial, J.-R., Su, W., Zhu, H.: Formalizing hybrid systems with Event-B. In: Derrick, J., Fitzgerald, J., Gnesi, S., Khurshid, S., Leuschel, M., Reeves, S., Riccobene, E. (eds.) ABZ 2012. LNCS, vol. 7316, pp. 178–193. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138(1), 3–34 (1995)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Alur, R., Henzinger, T.A., Lafferriere, G., Pappas, G.J.: Discrete abstractions of hybrid systems. Proc. of the IEEE 88, 971–984 (2000)CrossRefGoogle Scholar
  5. 5.
    Bouissou, O., Goubault, E., Putot, S., Tekkal, K., Vedrine, F.: HybridFluctuat: A static analyzer of numerical programs within a continuous environment. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 620–626. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    de Moura, L., Rueß, H., Sorea, M.: Bounded model checking and induction: From refutation to verification. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 14–26. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Dijkstra, E.W.: Guarded commands, nondeterminacy and formal derivation of programs. Communications of the ACM 18(8), 453–457 (1975)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past HyTech. International Journal on Software Tools for Technology Transfer (STTT) 10(3), 263–279 (2008)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ghosh, R., Tiwari, A., Tomlin, C.J.: Automated symbolic reachability analysis; with application to delta-notch signaling automata. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 233–248. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Hasuo, I., Suenaga, K.: Exercises in nonstandard static analysis of hybrid systems. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 462–478. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Henzinger, T.A.: The theory of hybrid automata. Verification of Digital and Hybrid Systems (NATO ASI Series F: Computer and Systems Sciences) 170, 265–292 (2000)CrossRefGoogle Scholar
  12. 12.
    Henzinger, T.A., Ho, P.H., Wong-Toi, H.: HyTech: A model checker for hybrid systems. STTT 1, 110–122 (1997)MATHCrossRefGoogle Scholar
  13. 13.
    Hoare, C.A.R.: An axiomatic basis for computer programming. Communications of the ACM 12(10), 576–580, 583 (1969)Google Scholar
  14. 14.
    Jha, S.K., Krogh, B.H., Weimer, J.E., Clarke, E.M.: Reachability for linear hybrid automata using iterative relaxation abstraction. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 287–300. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Manna, Z., Sipma, H.: Deductive verification of hybrid systems using STeP. In: Henzinger, T.A., Sastry, S.S. (eds.) HSCC 1998. LNCS, vol. 1386, pp. 305–318. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  16. 16.
    Platzer, A.: Logical Analysis of Hybrid Systems. Springer (2010)Google Scholar
  17. 17.
    Platzer, A.: Guide for KeYmaera hybrid systems verification tool (2012), http://symbolaris.com/info/KeYmaera-guide.html (accessed January 1, 2013)
  18. 18.
    Platzer, A., Quesel, J.-D.: KeYmaera: A hybrid theorem prover for hybrid systems (System description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 171–178. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Rodríguez-Carbonell, E., Tiwari, A.: Generating polynomial invariants for hybrid systems. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 590–605. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  20. 20.
    Sankaranarayanan, S., Sipma, H.B., Manna, Z.: Constructing invariants for hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 539–554. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  21. 21.
    Su, W., Abrial, J.-R., Zhu, H.: Complementary methodologies for developing hybrid systems with event-B. In: Aoki, T., Taguchi, K. (eds.) ICFEM 2012. LNCS, vol. 7635, pp. 230–248. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  22. 22.
    Tiwari, A.: HybridSAL relational abstracter. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 725–731. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Daisuke Ishii
    • 1
  • Guillaume Melquiond
    • 2
  • Shin Nakajima
    • 1
  1. 1.National Institute of InformaticsChiyoda-kuJapan
  2. 2.INRIA Saclay–Île-de-France, LRI, bât 650Université Paris Sud 11OrsayFrance

Personalised recommendations