Advertisement

Assertion-Based Analysis of Hybrid Systems with PVS

  • Erika Ábrahám-Mumm
  • Ulrich Hannemann
  • Martin Steffen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2178)

Abstract

Hybrid systems are a well-established mathematical model for embedded systems. Such systems, which combine discrete and continuous behavior, are increasingly used in safety-critical applications. To guarantee safe functioning, formal verification techniques are crucial. While research in this area concentrates on model checking, deductive techniques attracted less attention. In this paper we use the general purpose theorem prover PVS for the rigorous formalization and analysis of hybrid systems. To allow for machine-assisted proofs, we implement a deductive assertional proof method within PVS. The sound and complete proof system allows modular proofs in that it comprises a proof rule for the parallel composition. Besides hybrid systems and the proof system, a number of examples are formalized within PVS.

Keywords

hybrid systems deductive methods machine-assisted verification 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. Ábrahfm-Mumm, U. Hannemann, and M. Steffen. Verification of hybrid systems: Formalization and proof rules in PVS. Technical Report TR-ST-01-1, Lehrstuhl für Software-Technologie, Institut für Informatik und praktische Mathematik, Christian-Albrechts-Universität Kiel, Jan. 2001.Google Scholar
  2. [2]
    R. Alur, C. Courcoubetis, T. Henzinger, P. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138:3–34, 1995. A preliminary version appeared in the proceedings of 11th. International Conference on Analysis and Optimization of Systems: Discrete Event Systems (LNCI 199).zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    R. Alur and D. Dill. A theory of timed automata. Theoretical Computer Science, 126:252–235, 1994.CrossRefMathSciNetGoogle Scholar
  4. [4]
    R. Alur, T. A. Henzinger, and P. Ho. Automatic symbolic verification of embedded systems. In Proc. 14th Annual Real-Time Systems Symposium, pages 2–11. IEEE Computer Society Press, 1993.Google Scholar
  5. [5]
    M. Archer and C. Heitmeyer. Verifying hybrid systems modeled as timed automata: A case sudy. In O. Maler, editor, Hybrid and Real-Time Systems (HART’97), number 1201 in Lecture Notes in Computer Science, pages 171–185. Springer-Verlag, 1997.CrossRefGoogle Scholar
  6. [6]
    E. M. Clarke, O. Grumberg, and D. Peled. Model Checking. MIT Press, 1999.Google Scholar
  7. [7]
    The Coq project. http://pauillac.inria.fr/coq/, 1998.
  8. [8]
    J. B. de Meer and E. Ábrahám-Mumm. Formal methods for reflective system specification. In J. Grabowski and S. Heymer, editors, Formale Beschreibungstechniken für verteilte Systeme, pages 51–57. Universität Lübeck/Shaker Verlag, Aachen, Juni 2000 2000.Google Scholar
  9. [9]
    W.-P. de Roever, F. de Boer, U. Hannemann, J. Hooman, Y. Lakhnech, M. Poel, and J. Zwiers. Concurrency Verification: Introduction to Compositional and Noncompositional Proof Methods. Cambridge University Press, 2001. to appear.Google Scholar
  10. [10]
    R. W. Floyd. Assigning meanings to programs. In J. T. Schwartz, editor, Proc. Symp. In Applied Mathematics, volume 19, pages 19–32, 1967.Google Scholar
  11. [11]
    M. J. C. Gordon and T. F. Melham, editors. Introduction to HOL: A Theorem Proving Environment for Higher-Order Logic. Cambridge University Press, 1993.Google Scholar
  12. [12]
    R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, editors. Hybrid Systems, volume 736 of Lecture Notes in Computer Science. Springer-Verlag, 1993.Google Scholar
  13. [13]
    U. Hannemann. Semantic Analysis of Compositional Proof Methods for Concurrency. PhD thesis, Utrecht Universiteit, Oct. 2000.Google Scholar
  14. [14]
    T. Henzinger and H. Wong-Toi. Linear phase-portrait approximations for nonlinear hybrid systems. In R. Alur, T. Henzinger, and E. D. Sontag, editors, Hybrid Systems III, volume 1066 of Lecture Notes in Computer Science, pages 377–388, 1996.CrossRefGoogle Scholar
  15. [15]
    T. A. Henzinger and P.-H. Ho. Algorithmic analysis of nonlinear hybrid systems. In P. Wolper, editor, CAV’ 95: Computer Aided Verification, volume 939 of Lecture Notes in Computer Science, pages 225–238. Springer-Verlag, 1995.Google Scholar
  16. [16]
    T. A. Henzinger, P. W. Kopke, A. Puri, and P. Varaiya. What’s decidable about hybrid automata. In 27th Annual ACM Symposium on Theory of Computing. ACM Press, 1995.Google Scholar
  17. [17]
    T. A. Henzinger and V. Rusu. Reachability verification for hybrid automata. In Henzinger and Sastry [18], pages 190–204.Google Scholar
  18. [18]
    T. A. Henzinger and S. Sastry, editors. Proceedings of the First International Workshop on Hybrid Systems: Computation and Control (HSCC’98), volume 1386 of Lecture Notes in Computer Science. Springer, 1998.Google Scholar
  19. [19]
    J. Hooman. A compositional approach to the design of hybrid systems. In Grossman et al. [12], pages 121–148.Google Scholar
  20. [20]
    A. Kapur, T. A. Henzinger, Z. Manna, and A. Pnueli. Proving safety properties of hybrid systems. In H. Langmaack, W.-P. de Roever, and J. Vytopil, editors, Formal Techniques in Real-Time and Fault-Tolerant Systems 1994, volume 863 of Lecture Notes in Computer Science, Kiel, Germany, September 1994. Springer-Verlag. 3rd International School and Symposium.Google Scholar
  21. [21]
    Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine. Integration graphs: a class of decidable hybrid systems. In Grossman et al. [12], pages 179–208.Google Scholar
  22. [22]
    S. Kowalewski, P. Herrmann, S. Engell, H. Krumm, H. Treseler, Y. Lakhnech, R. Huuck, and B. Lukoschus. Approaches to the formal verification of hybrid systems. at Automatisierungstechnik. Special Issue: Hybrid Systems II: Analysis, Modeling, and Verification, 49(2):66–74, Feb. 2001.Google Scholar
  23. [23]
    N. A. Lynch, R. Segala, and F. W. Vaandrager. Hybrid I/O automata revisited. In M. D. D. Benedetto and A. Sangiovanni-Vincentelli, editors, Proceedings of the 4th International Wokrshop on Hybrid Systems: Computation and Control (HSCC 2001), Rome, volume 2034 of Lecture Notes in Computer Science. Springer-Verlag, 2001.Google Scholar
  24. [24]
    Z. Manna and H. B. Sipma. Deductive verification of hybrid systems using STeP. In Henzinger and Sastry [18].Google Scholar
  25. [25]
    S. Owre, J. M. Rushby, and N. Shankar. PVS: A prototype verification system. In D. Kapur, editor, Automated Deduction (CADE-11), volume 607 of Lecture Notes in Computer Science, pages 748–752. Springer-Verlag, 1992.Google Scholar
  26. [26]
    S. Owre, N. Shankar, J. M. Rushby, and D.W. J. Stringer-Calvert. PVS Manual (Language Reference, Prover Guide, System Guide). Computer Science Laboratory, SRI International, Menlo Park, CA, Sept. 1999.Google Scholar
  27. [27]
    L. C. Paulson. The Isabelle reference manual. Technical Report 283, University of Cambridge, Computer Laboratory, 1993.Google Scholar
  28. [28]
    O. Roux and V. Rusu. Uniformity for the decidability of hybrid automata. In R. Cousot and D. A. Schmidt, editors, Proceedings of SAS’ 96, volume 1145 of Lecture Notes in Computer Science, pages 301–316. Springer-Verlag, 1996.Google Scholar
  29. [29]
    J. M. Rushby, 2001. available electronically at http://www.csl.sri.com/papers/pvs-bib/
  30. [30]
    N. Shankar. Lazy compositional verification. In W.-P. de Roever, H. Langmaack, and A. Pnueli, editors, Compositionality: The Significant Difference (Compos’ 97), volume 1536 of Lecture Notes in Computer Science, pages 541–564. Springer, 1998.CrossRefGoogle Scholar
  31. [31]
    T. Stauner. Properties of hybrid systems-a computer science perspective. Technical Report TUM-I0017, Technische Universität München, Nov. 2000.Google Scholar
  32. [32]
    T. Stauner. Hybrid systems’ properties-classification and relation to computer science. In Proceedings of the Eight International Conference on Computer Aided Systems Theory, Formal Methods and Tools for Computer Science (Eurocast’ 01), Lecture Notes in Computer Science. Springer-Verlag, 2001.Google Scholar
  33. [33]
    J. Vitt and J. Hooman. Assertional specification and verification using PVS of the steam boiler system. In Formal Methods for Industrial Applications: Specifying and Programmin the Steam Boiler Control System, volume 1165 of Lecture Notes in Computer Science, pages 453–472. Springer, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Erika Ábrahám-Mumm
    • 1
  • Ulrich Hannemann
    • 2
  • Martin Steffen
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität zu KielKielDeutschland
  2. 2.Computing Science DepartmentUniversity of NijmegenGL NijmegenThe Netherlands

Personalised recommendations