Exercises in Nonstandard Static Analysis of Hybrid Systems

  • Ichiro Hasuo
  • Kohei Suenaga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7358)

Abstract

In formal verification of hybrid systems, a big challenge is to incorporate continuous flow dynamics in a discrete framework. Our previous work proposed to use nonstandard analysis (NSA) as a vehicle from discrete to hybrid; and to verify hybrid systems using a Hoare logic. In this paper we aim to exemplify the potential of our approach, through transferring static analysis techniques to hybrid applications. The transfer is routine via the transfer principle in NSA. The techniques are implemented in our prototype automatic precondition generator.

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References

  1. 1.
    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. Theor. Comp. Sci. 138(1), 3–34 (1995)MATHCrossRefGoogle Scholar
  2. 2.
    Balakrishnan, G., Sankaranarayanan, S., Ivancic, F., Gupta, A.: Refining the control structure of loops using static analysis. In: EMSOFT, pp. 49–58 (2009)Google Scholar
  3. 3.
    Benveniste, A., Bourke, T., Caillaud, B., Pouzet, M.: Non-standard semantics of hybrid systems modelers. J. Comput. Syst. Sci. 78(3), 877–910 (2012)CrossRefGoogle Scholar
  4. 4.
    Beyer, D., Henzinger, T.A., Majumdar, R., Rybalchenko, A.: Path invariants. In: Ferrante, J., McKinley, K.S. (eds.) PLDI, pp. 300–309. ACM (2007)Google Scholar
  5. 5.
    Bliudze, S., Krob, D.: Modelling of complex systems: Systems as dataflow machines. Fundam. Inform. 91(2), 251–274 (2009)MathSciNetMATHGoogle Scholar
  6. 6.
    Chaudhuri, S., Gulwani, S., Lublinerman, R., NavidPour, S.: Proving programs robust. In: Gyimóthy, T., Zeller, A. (eds.) SIGSOFT FSE, pp. 102–112. ACM (2011)Google Scholar
  7. 7.
    Colón, M.A., Sankaranarayanan, S., Sipma, H.B.: Linear Invariant Generation Using Non-linear Constraint Solving. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 420–432. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Gamboa, R.A., Kaufmann, M.: Nonstandard analysis in ACL2. J. Autom. Reason. 27(4), 323–351 (2001)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Goldblatt, R.: Lectures on the Hyperreals: An Introduction to Nonstandard Analysis. Springer (1998)Google Scholar
  10. 10.
    Gopan, D., Reps, T.: Guided Static Analysis. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 349–365. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Hasuo, I., Suenaga, K.: Exercises in Nonstandard Static Analysis of hybrid systems. Extended version with proofs (2012), www-mmm.is.s.u-tokyo.ac.jp/~ichiro
  12. 12.
    Hurd, A.E., Loeb, P.A.: An Introduction to Nonstandard Real Analysis. Academic Press (1985)Google Scholar
  13. 13.
    Platzer, A.: Differential-algebraic dynamic logic for differential-algebraic programs. J. Log. Comput. 20(1), 309–352 (2010)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Platzer, A.: Logical Analysis of Hybrid Systems—Proving Theorems for Complex Dynamics. Springer (2010)Google Scholar
  15. 15.
    Platzer, A.: The complete proof theory of hybrid systems. Tech. Rep. CMU–CS–11–144, Carnegie-Mellon Univ., Pittsburgh PA 15213 (2011)Google Scholar
  16. 16.
    Robinson, A.: Non-standard analysis, revised edn. Princeton University Press (1996)Google Scholar
  17. 17.
    Rodríguez-Carbonell, E., Tiwari, A.: Generating Polynomial Invariants for Hybrid Systems. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 590–605. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Sankaranarayanan, S.: Automatic invariant generation for hybrid systems using ideal fixed points. In: Johansson, K.H., Yi, W. (eds.) HSCC, pp. 221–230. ACM (2010)Google Scholar
  19. 19.
    Sankaranarayanan, S., Sipma, H., Manna, Z.: Non-linear loop invariant generation using gröbner bases. In: Jones, N.D., Leroy, X. (eds.) POPL, pp. 318–329. ACM (2004)Google Scholar
  20. 20.
    Sankaranarayanan, S., Sipma, H.B., Manna, Z.: Constructing invariants for hybrid systems. Formal Methods in System Design 32(1), 25–55 (2008)MATHCrossRefGoogle Scholar
  21. 21.
    Sharma, R., Dillig, I., Dillig, T., Aiken, A.: Simplifying Loop Invariant Generation Using Splitter Predicates. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 703–719. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  22. 22.
    Suenaga, K., Hasuo, I.: Programming with Infinitesimals: A While-Language for Hybrid System Modeling. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 392–403. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  23. 23.
    Winskel, G.: The Formal Semantics of Programming Languages. MIT Press (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ichiro Hasuo
    • 1
  • Kohei Suenaga
    • 2
  1. 1.University of TokyoJapan
  2. 2.Kyoto UniversityJapan

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