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Exact State Set Representations in the Verification of Linear Hybrid Systems with Large Discrete State Space

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Automated Technology for Verification and Analysis (ATVA 2007)

Abstract

We propose algorithms significantly extending the limits for maintaining exact representations in the verification of linear hybrid systems with large discrete state spaces. We use AND-Inverter Graphs (AIGs) extended with linear constraints (LinAIGs) as symbolic representation of the hybrid state space, and show how methods for maintaining compactness of AIGs can be lifted to support model-checking of linear hybrid systems with large discrete state spaces. This builds on a novel approach for eliminating sets of redundant constraints in such rich hybrid state representations by a suitable exploitation of the capabilities of SMT solvers, which is of independent value beyond the application context studied in this paper. We used a benchmark derived from an Airbus flap control system (containing 220 discrete states) to demonstrate the relevance of the approach.

This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS, http://www.avacs.org/).

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References

  1. Agrawal, M., Thiagarajan, P.S.: Lazy rectangular hybrid automata. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 1–15. Springer, Heidelberg (2004)

    Google Scholar 

  2. Agrawal, M., Thiagarajan, P.S.: The discrete time behavior of lazy linear hybrid automata. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 55–69. Springer, Heidelberg (2005)

    Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  4. Asarin, E., Dang, T., Girard, A.: Hybridization methods for the analysis of non-linear systems. Acta Informatica 43(7), 451–476 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Asarin, E., Dang, T., Maler, O.: The d/dt tool for verification of the hybrid systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 365–370. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  6. Boigelot, B., Herbreteau, F.: The power of hybrid acceleration. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 438–451. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Damm, W., Disch, S., Hungar, H., Pang, J., Pigorsch, F., Scholl, C., Waldmann, U., Wirtz, B.: Automatic verification of hybrid systems with large discrete state space. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 276–291. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  8. Damm, W., Pinto, G., Ratschan, S.: Guaranteed termination in the verification of LTL properties of non-linear robust discrete time hybrid systems. Journal of Foundations of Computer Science 18(1), 63–86 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dolzmann, A.: Algorithmic Strategies for Applicable Real Qunantifier Elimination. PhD thesis, Universität Passau (2000)

    Google Scholar 

  10. Fränzle, M., Herde, C.: HySAT: An efficient proof engine for bounded model checking of hybrid systems. Formal Methods in System Design 30(3), 179–198 (2007)

    Article  MATH  Google Scholar 

  11. Frehse, G.: Compositional Verification of Hybrid Systems using Simulation Relations. PhD thesis, Radboud Universiteit Nijmegen (2005)

    Google Scholar 

  12. Girard, A., Pappas, G.J.: Approximation metrics for discrete and continuous systems. IEEE Transactions on Automatic Control 52(5), 782–798 (2007)

    Article  MathSciNet  Google Scholar 

  13. H3 FOMC Team. The flap controller description, http://www.avacs.org/Benchmarks/flapcontroller.pdf

  14. Henzinger, T.A.: The theory of hybrid automata. In: 11th IEEE Symposium on Logic in Computer Science, pp. 278–292. IEEE Press, Los Alamitos (1996)

    Chapter  Google Scholar 

  15. Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: HyTech: A model checker for hybrid systems. Software Tools for Technology Transfer 1(1–2), 110–122 (1997)

    Article  MATH  Google Scholar 

  16. Hoare, C.A.R.: An axiomatic basis for computer programming. Communication of the ACM 12, 576–583 (1969)

    Article  MATH  Google Scholar 

  17. Jha, S., Brady, B., Seshia, S.: Symbolic reachability analysis of lazy linear hybrid automata. Technical report, EECS Dept. UC Berkeley (2007)

    Google Scholar 

  18. Kuehlmann, A., Paruthi, V., Krohm, F., Ganai, M.K.: Robust boolean reasoning for equivalence checking and functional property verification. IEEE Transactions on Computer-Aided Design 21(12), 1377–1394 (2002)

    Article  Google Scholar 

  19. Loos, R., Weispfenning, V.: Applying linear quantifier elimination. The Computer Journal 36(5), 450–462 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  20. McMillan, K.L.: Symbolic Model Checking. Kluwer Academic Publishers, Dordrecht (1993)

    MATH  Google Scholar 

  21. Mishchenko, A., Chatterjee, S., Jiang, R., Brayton, R.K.: FRAIGs: A unifying representation for logic synthesis and verification. Technical report, EECS Dept. UC Berkeley (2005)

    Google Scholar 

  22. Paruthi, V., Kuehlmann, A.: Equivalence checking combining a structural SAT-solver, BDDs, and simulation. In: 18th IEEE Conference on Computer Design, pp. 459–464. IEEE Press, Los Alamitos (2000)

    Google Scholar 

  23. Pigorsch, F., Scholl, C., Disch, S.: Advanced unbounded model checking by using AIGs, BDD sweeping and quantifier scheduling. In: 6th Conference on Formal Methods in Computer Aided Design, pp. 89–96. IEEE Press, Los Alamitos (2006)

    Chapter  Google Scholar 

  24. Platzer, A., Clarke, E.: The image computation problem in hybrid systems model checking. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. 10th Workshop on Hybrid Systems: Computation and Control. LNCS, vol. 4416, pp. 473–486. Springer, Heidelberg (2007)

    Google Scholar 

  25. Segelken, M.: Abstraction and counterexample-guided construction of ω-automata for model checking of step-discrete linear hybrid models. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 433–448. Springer, Heidelberg (2007)

    Google Scholar 

  26. Silva, B.I., Richeson, K., Krogh, B.H., Chutinan, A.: Modeling and verification of hybrid dynamical system using CheckMate. In: 4th Conference on Automation of Mixed Processes (2000)

    Google Scholar 

  27. The VIS Group. VIS: A system for verification and synthesis. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 428–432. Springer, Heidelberg (1996)

    Google Scholar 

  28. Wang, F.: Symbolic parametric safety analysis of linear hybrid systems with BDD-like data-structures. IEEE Transactions on Software Engineering 31(1), 38–52 (2005)

    Article  Google Scholar 

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Kedar S. Namjoshi Tomohiro Yoneda Teruo Higashino Yoshio Okamura

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Damm, W. et al. (2007). Exact State Set Representations in the Verification of Linear Hybrid Systems with Large Discrete State Space . In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds) Automated Technology for Verification and Analysis. ATVA 2007. Lecture Notes in Computer Science, vol 4762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75596-8_30

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  • DOI: https://doi.org/10.1007/978-3-540-75596-8_30

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