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Property Driven Three-Valued Model Checking on Hybrid Automata

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Book cover Logic, Language, Information and Computation (WoLLIC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5514))

Abstract

In this paper, we present a three-valued property driven model checking algorithm for the logic CTL on hybrid automata. The technique of multi-valued model checking for hybrid automata aims at combining the advantages of classical methods based either on the preorder of simulation or on bounded reachability. However, as originally defined, it relies on the preliminary definition of special abstractions for combined over- and under-approximated reachability analysis, whose size is crucial and can be infinite. Our procedure avoids the above problem, since it is based on an incremental construction of the abstraction for the original hybrid automaton, that is suitably driven by the property under consideration.

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References

  1. Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alur, R., Henzinger, T., Ho, P.-H.: Automatic symbolic verification of embedded systems. IEEE Transactions on Software Engineering 22(3), 181–201 (1996)

    Article  Google Scholar 

  3. Alur, R., Henzinger, T., Lafferriere, G., Pappas, G.: Discrete abstractions of hybrid systems. Proceedings of the IEEE 88(7), 971–984 (2000)

    Article  Google Scholar 

  4. Bauer, K., Gentilini, R., Schneider, K.: A uniform approach to three-valued semantics for μ-calculus on abstractions of hybrid automata. In: Hu, A., Chockler, H. (eds.) Haifa Verification Conference (HVC), Haifa, Israel. LNCS. Springer, Heidelberg (2008)

    Google Scholar 

  5. Brihaye, T., Michaux, C., Rivière, C., Troestler, C.: On O-minimal hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 219–233. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  6. Fränzle, M.: What will be eventually true of polynomial hybrid automata? In: Kobayashi, N., Pierce, B.C. (eds.) TACS 2001. LNCS, vol. 2215, pp. 340–359. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Gentilini, R., Schneider, K., Mishra, B.: Successive abstractions of hybrid automata for monotonic CTL model checking. In: Artemov, S.N., Nerode, A. (eds.) LFCS 2007. LNCS, vol. 4514, pp. 224–240. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Ghosh, R., Tiwari, A., Tomlin, C.: 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)

    Chapter  Google Scholar 

  9. Ghosh, R., Tomlin, C.: Lateral inhibition through delta-notch signaling: A piecewise affine hybrid model. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 232–245. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  10. Henzinger, M., Henzinger, T., Kopke, P.: Computing simulations on finite and infinite graphs. In: Seberry, J., Pieprzyk, J. (eds.) Annual Symposium on Foundations of Computer Science (FOCS), p. 453. IEEE Computer Society Press, Los Alamitos (1995)

    Google Scholar 

  11. Henzinger, T.: The theory of hybrid automata. In: Verification of Digital and Hybrid Systems. NATO Advanced Study Institute Series F: Computer and Systems Sciences, vol. 170, pp. 265–292. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  12. Henzinger, T., Kopke, P., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? Journal of Computer and System Sciences 57(1), 94–124 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kleene, S.: Introduction to Metamathematics. North-Holland, Amsterdam (1952)

    MATH  Google Scholar 

  14. Lafferriere, G., Pappas, G., Sastry, S.: O-minimal hybrid systems. Mathematics of Control, Signals, and Systems 13(1), 1–21 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Lafferriere, G., Pappas, J., Yovine, S.: A new class of decidable hybrid systems. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 137–151. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  16. Miller, J.: Decidability and complexity results for timed automata and semi-linear hybrid automata. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 296–309. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  17. Piazza, C., Antoniotti, M., Mysore, V., Policriti, A., Winkler, F., Mishra, B.: Algorithmic algebraic model checking I: Challenges from systems biology. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 5–19. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. 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)

    Chapter  Google Scholar 

  19. Tiwari, A., Khanna, G.: Series of abstractions for hybrid automata. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, pp. 465–478. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

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Bauer, K., Gentilini, R., Schneider, K. (2009). Property Driven Three-Valued Model Checking on Hybrid Automata. In: Ono, H., Kanazawa, M., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2009. Lecture Notes in Computer Science(), vol 5514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02261-6_18

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  • DOI: https://doi.org/10.1007/978-3-642-02261-6_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02260-9

  • Online ISBN: 978-3-642-02261-6

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