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Deductive verification of hybrid systems using step

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Hybrid Systems: Computation and Control (HSCC 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1386))

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Abstract

We investigate the feasibility of computer-aided deductive verification of hybrid systems. Hybrid systems are modeled by phase transition systems, in which activities specify the bounds on the derivatives of the continuous variables. We present a method for invariant generation based on static analysis of the phase transition system. The invariants produced can be used as auxiliary properties in the verification of temporal properties. We show that in some cases the invariants thus produced suffice to prove the main safety property.

This research was supported in part by the National Science Foundation under grant CCR-95-27927, the Defense Advanced Research Projects Agency under NASA grant NAG2-892, ARO under grant D AAH04-95-1-0317, ARO under MURI grant DAAH04-96-1-0341, and by Army contract DABT63-96-C-0096 (DARPA).

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References

  1. Abrial, J. R., Börger, E., and Langmaack, H., Eds. Formal Methods for Industrial Applications, vol. 1163 of LNCS. Springer-Verlag, 1996.

    Google Scholar 

  2. Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T. A., HO, P.H., Nicollin, X., Olivero, A., Sifakis, J., and Yovine, S. The algorithmic analysis of hybrid systems. Theoretical Computer Science 138, 1 (1995), 3–34.

    Google Scholar 

  3. Alur, R., Courcoubetis, C., Henzlvger, T. A., and Ho, P.-H. Hybrid automata: An algorithmic approach to the specification and analysis of hybrid systems. In Grossman et al. [15], pp. 209–229.

    Google Scholar 

  4. Alur, R., and Henzinger, T. A., Eds. Proc. 8th Intl. Conference on Computer Aided Verification (July 1996), vol. 1102 of LNCS, Springer-Verlag.

    Google Scholar 

  5. Alur, R., Henzinger, T. A., and Ho, P. Automatic symbolic verification of embedded systems. IEEE Trans. Software Engin. 22, 3 (Mar. 1996), 181–201.

    Google Scholar 

  6. Archer, M., and Heitmeyer, C. Verifying hybrid systems modeled as timed automata: A case study. In Proc. 1st Intl. Workshop Hybrid and Real-time Systems (HART) (1997), O. Maler, Ed., vol. 1201 of LNCS, Springer-Verlag.

    Google Scholar 

  7. Bensalem, S., Lakhnech, Y., and Saidi, H. Powerful Techniques for the Automatic Generation of Invariants. In Alur and Henzinger [4], pp. 323–335.

    Google Scholar 

  8. Bjørner, N. S., Browne, A., Chang, E. S., Colón, M., Kapur, A., Manna, Z., Sipma, H. B., and Urige, T. E. STeP: Deductive-algorithmic verification of reactive and real-time systems. In Alur and Henzinger [4], pp. 415–418.

    Google Scholar 

  9. Bjørner, N. S., Browne, A., Chang, E. S., Colón, M., Kapur, A., Manna, Z., Sipma, H. B., and Urige, T. E. STeP: The Stanford Temporal Prover, User's Manual. Tech. Rep. STAN-CS-TR-95-1562, Computer Science Department, Stanford University, Nov. 1995.

    Google Scholar 

  10. Bjørner, N. S., Browne, A., and Manna, Z. Automatic generation of invariants and intermediate assertions. Theoretical Computer Science 173, 1 (Feb. 1997), 49–87. Preliminary version appeared in 1st Intl. Conf. on Principles and Practice of Constraint Programming, vol. 976 of LNCS, pp. 589–623, Springer-Verlag, 1995.

    Google Scholar 

  11. Bjor:nier, N. S., Manna, Z., Sipma, H. B., and Urige, T. E. Deductive verification of real-time systems using STeP. In 4th Intl. AMAST Workshop on Real-Time Systems (May 1997), vol. 1231 of LNCS, Springer-Verlag, pp. 22–43.

    Google Scholar 

  12. Bjørner, N. S., Stickel, M. E., and Urige, T. E. A practical integration of first-order reasoning and decision procedures. In Proc. of the 14thIntl. Conference on Automated Deduction (July 1997), vol. 1249 of LNCS, Springer-Verlag, pp. 101-115.

    Google Scholar 

  13. Dolzmann, A., and Sturm, T. REDLOG: Computer algebra meets computer logic. ACM SIGSAM Bulletin 31, 2 (June 1997), 2–9.

    Google Scholar 

  14. für Informationstechnik Berlin, K. Z. Z. REDUCE symbolic math system. http://vvv.zib.de/Symbolik/reduce/,1995.

    Google Scholar 

  15. Grossmau, R. L., Nerode, A., Raun, A. P., and Rischel, H., Eds. Hybrid Systems (1993), vol. 736 of LNCS, Springer-Verlag.

    Google Scholar 

  16. Henzinger, T. A. The theory of hybrid automata. In Proc. 11th IEEE Symp. Logic in Comp. Sci. (1996), IEEE Computer Society Press, pp. 278–292.

    Google Scholar 

  17. Henzinger, T. A., and Ho, P. Algorithmic analysis of nonlinear hybrid systems. In Wolper [27], pp. 225–238.

    Google Scholar 

  18. Henzlnger, T. A., Ho, P., and Wong-Toi, H. A user guide to HYTECH. In TACAS 95: First Intl. Workshop on Tools and Algorithms for the Construction and Analysis of Systems (1995), E. Brinksma. W. Cleaveland, K. Larsen, T. Margaria, and B. Steffen, Eds., vol. 1019 of LNCS, Springer-Verlag, pp. 41–71.

    Google Scholar 

  19. Henzinger, T. A., and Wong-Toi, H. Linear phase-portrait approximations for nonlinear hybrid systems. In Hybrid Systems III (1996), R. Alur, T. A. Henzinger, and E. D. Sontag, Eds., vol. 1066 of LNCS, Springer-Verlag, pp. 377–388.

    Google Scholar 

  20. Henzinger, T. A., and Wong-Toi, H. Using HyTECII to synthesize control parameters for a steam boiler. In Abrial et al. [1].

    Google Scholar 

  21. Ho, P.-H., and Wong-Toi, H. Automated analysis of an audio control protocol. In Wolper [27], pp. 381–394.

    Google Scholar 

  22. Manna, Z., and Pnueli, A. Clocked transition systems. In Proc. of the Intl. Logic and Software Engineering Workshop (Aug. 1995). Beijing, China.

    Google Scholar 

  23. Manna, Z., and Pnueli, A. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, 1995.

    Google Scholar 

  24. Nicollin, X., Olivero, A., Sifakis, J., and Yovine, S. An approach to the description and analysis of hybrid systems. In Grossman et al. [15], pp. 149–178.

    Google Scholar 

  25. Su, J. X., Dill, D. L., and Barrett, C. W. Automatic generation of invariants for processor verification. In 1st Intl. Conf. on Formal Methods in Computer-Aided Design (Nov. 1996), vol. 1166 of LNCS, Springer-Verlag, pp. 377–388.

    Google Scholar 

  26. Vitt, J., and Hooman, J. Assertional specification and verification using PVS of the steam boiler control system. In Abrial et al. [1], pp. 453–472.

    Google Scholar 

  27. Wolper, P., Ed. Proc. 7thIntl. Conference on Computer Aided Verification (July 1995), vol. 939 of LNCS.

    Google Scholar 

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Authors and Affiliations

  1. Computer Science Department, Stanford University, 94305, Stanford, CA

    Zohar Manna & Henny B. Sipma

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  1. Zohar Manna
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  2. Henny B. Sipma
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Thomas A. Henzinger Shankar Sastry

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Manna, Z., Sipma, H.B. (1998). Deductive verification of hybrid systems using step. In: Henzinger, T.A., Sastry, S. (eds) Hybrid Systems: Computation and Control. HSCC 1998. Lecture Notes in Computer Science, vol 1386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-64358-3_47

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  • DOI: https://doi.org/10.1007/3-540-64358-3_47

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  • Print ISBN: 978-3-540-64358-6

  • Online ISBN: 978-3-540-69754-1

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