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Falsification of LTL Safety Properties in Hybrid Systems

  • Erion Plaku
  • Lydia E. Kavraki
  • Moshe Y. Vardi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5505)

Abstract

This paper develops a novel computational method for the falsification of safety properties specified by syntactically safe linear temporal logic (LTL) formulas φ for hybrid systems with general nonlinear dynamics and input controls. The method is based on an effective combination of robot motion planning and model checking. Experiments on a hybrid robotic system benchmark with nonlinear dynamics show significant speedup over related work. The experiments also indicate significant speedup when using minimized DFA instead of non-minimized NFA, as obtained by standard tools, for representing the violating prefixes of φ.

References

  1. 1.
    Tomlin, C.J., Mitchell, I., Bayen, A., Oishi, M.: Computational techniques for the verification and control of hybrid systems. Proc. of IEEE 91(7), 986–1001 (2003)CrossRefzbMATHGoogle Scholar
  2. 2.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Henzinger, T., Kopke, P., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? In: ACM Symp. on Theory of Computing, pp. 373–382 (1995)Google Scholar
  4. 4.
    Mitchell, I.M.: Comparing forward and backward reachability as tools for safety analysis. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 428–443. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Alur, R., Henzinger, T.A., Lafferriere, G., Pappas, G.: Discrete abstractions of hybrid systems. Proc. of IEEE 88(7), 971–984 (2000)CrossRefGoogle Scholar
  6. 6.
    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. Intl. J. of Foundations of Computer Science 14(4), 583–604 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Giorgetti, N., Pappas, G.J., Bemporad, A.: Bounded model checking for hybrid dynamical systems. In: Conf. on Decision & Control, Seville, Spain, pp. 672–677 (2005)Google Scholar
  8. 8.
    Bhatia, A., Frazzoli, E.: Incremental search methods for reachability analysis of continuous and hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 142–156. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Kim, J., Esposito, J.M., Kumar, V.: An RRT-based algorithm for testing and validating multi-robot controllers. In: Robotics: Science & Systems, Boston, MA, pp. 249–256 (2005)Google Scholar
  10. 10.
    Nahhal, T., Dang, T.: Test coverage for continuous and hybrid systems. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 449–462. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Plaku, E., Kavraki, L.E., Vardi, M.Y.: Hybrid systems: From verification to falsification. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 463–476. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Plaku, E., Kavraki, L.E., Vardi, M.Y.: Hybrid systems: From verification to falsification by combining motion planning and discrete search. Formal Methods in System Design (2008)Google Scholar
  13. 13.
    Copty, F., Fix, L., Fraer, R., Giunchiglia, E., Kamhi, G., Tacchella, A., Vardi, M.Y.: Benefits of bounded model checking at an industrial setting. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 436–453. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    LaValle, S.M., Kuffner, J.J.: Randomized kinodynamic planning. Intl. J. of Robotics Research 20(5), 378–400 (2001)CrossRefGoogle Scholar
  15. 15.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  16. 16.
    Behrmann, G., David, A., Larsen, K.G., Möller, O., Pettersson, P., Yi, W.: Uppaal present and future. In: Conf. on Decision & Control, Orlando, FL, pp. 2881–2886 (2001)Google Scholar
  17. 17.
    Fainekos, G.E., Kress-Gazit, H., Pappas, G.: Temporal logic motion planning for mobile robots. In: IEEE Intl. Conf. on Robotics & Automation, Barcelona, Spain, pp. 2020–2025 (2005)Google Scholar
  18. 18.
    Batt, G., Belta, C., Weiss, R.: Temporal logic analysis of gene networks under parameter uncertainty. IEEE Trans. of Automatic Control 53, 215–229 (2008)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Damm, W., Pinto, G., Ratschan, S.: Guaranteed termination in the verification of LTL properties of non-linear robust discrete time hybrid systems. Intl. J. of Foundations of Computer Science 18(1), 63–86 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Kupferman, O., Vardi, M.: Model checking of safety properties. Formal methods in System Design 19(3), 291–314 (2001)CrossRefzbMATHGoogle Scholar
  21. 21.
    Armoni, R., Egorov, S., Fraer, R., Korchemny, D., Vardi, M.: Efficient LTL compilation for SAT-based model checking. In: Intl. Conf. on Computer-Aided Design, San Jose, CA, pp. 877–884 (2005)Google Scholar
  22. 22.
    Sistla, A.: Safety, liveness and fairness in temporal logic. Formal Aspects of Computing 6, 495–511 (1994)CrossRefzbMATHGoogle Scholar
  23. 23.
    Choset, H., Lynch, K.M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L.E., Thrun, S.: Principles of Robot Motion: Theory, Algorithms, and Implementations. MIT Press, Cambridge (2005)zbMATHGoogle Scholar
  24. 24.
    LaValle, S.M.: Planning Algorithms. Cambridge University Press, Cambridge (2006)CrossRefzbMATHGoogle Scholar
  25. 25.
    Esposito, J., Kumar, V., Pappas, G.: Accurate event detection for simulation of hybrid systems. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 204–217. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  26. 26.
    Julius, A.A., Fainekos, G.E., Anand, M., Lee, I., Pappas, G.J.: Robust test generation and coverage for hybrid systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 329–342. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  27. 27.
    Plaku, E., Kavraki, L.E., Vardi, M.Y.: Discrete search leading continuous exploration for kinodynamic motion planning. In: Robotics: Science & Systems, Atlanta, GA (2007)Google Scholar
  28. 28.
    Fehnker, A., Ivančić, F.: Benchmarks for hybrid systems verification. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 326–341. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  29. 29.
    Latvala, T.: Efficient model checking of safety properties. In: Ball, T., Rajamani, S.K. (eds.) SPIN 2003. LNCS, vol. 2648, pp. 74–88. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  30. 30.
    Ladd, A.M.: Motion Planning for Physical Simulation. PhD thesis, Rice University, Houston, TX (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Erion Plaku
    • 1
  • Lydia E. Kavraki
    • 1
  • Moshe Y. Vardi
    • 1
  1. 1.Dept. of Computer ScienceRice UniversityHoustonUSA

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