Refinement of Trace Abstraction for Real-Time Programs

  • Franck Cassez
  • Peter Gjøl Jensen
  • Kim Guldstrand Larsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10506)

Abstract

Real-time programs are made of instructions that can perform assignments to discrete and real-valued variables. They are general enough to capture interesting classes of timed systems such as timed automata, stopwatch automata, time(d) Petri nets and hybrid automata. We propose a semi-algorithm using refinement of trace abstractions to solve both the reachability verification problem and the parameter synthesis problem for real-time programs. We report on the implementation of our algorithm and we show that our new method provides solutions to problems which are unsolvable by the current state-of-the-art tools.

References

  1. 1.
    Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    André, É., Fribourg, L., Kühne, U., Soulat, R.: IMITATOR 2.5: a tool for analyzing robustness in scheduling problems. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 33–36. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32759-9_6 CrossRefGoogle Scholar
  3. 3.
    André, É., Lipari, G., Nguyen, H.G., Sun, Y.: Reachability preservation based parameter synthesis for timed automata. In: Havelund, K., Holzmann, G., Joshi, R. (eds.) NFM 2015. LNCS, vol. 9058, pp. 50–65. Springer, Cham (2015). doi:10.1007/978-3-319-17524-9_5 Google Scholar
  4. 4.
    Behrmann, G., David, A., Larsen, K.G., Hakansson, J., Petterson, P., Yi, W., Hendriks, M.: Uppaal 4.0. In: QEST 2006, pp. 125–126 (2006)Google Scholar
  5. 5.
    Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: Comparison of the expressiveness of timed automata and time Petri nets. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 211–225. Springer, Heidelberg (2005). doi:10.1007/11603009_17 CrossRefGoogle Scholar
  6. 6.
    Beyer, D.: Competition on software verification. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 504–524. Springer, Heidelberg (2012). doi:10.1007/978-3-642-28756-5_38 CrossRefGoogle Scholar
  7. 7.
    Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: The expressive power of time Petri nets. Theor. Comput. Sci. 474, 1–20 (2013)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Byg, J., Jacobsen, M., Jacobsen, L., Jørgensen, K.Y., Møller, M.H., Srba, J.: TCTL-preserving translations from timed-arc Petri nets to networks of timed automata. TCS (2013). doi:10.1016/j.tcs.2013.07.011
  9. 9.
    Cassez, F., Larsen, K.: The impressive power of stopwatches. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 138–152. Springer, Heidelberg (2000). doi:10.1007/3-540-44618-4_12 CrossRefGoogle Scholar
  10. 10.
    Cassez, F., Roux, O.H.: Structural translation from time Petri nets to timed automata. J. Softw. Syst. 79(10), 1456–1468 (2006)CrossRefMATHGoogle Scholar
  11. 11.
    Cassez, F., Sloane, A.M., Roberts, M., Pigram, M., Suvanpong, P., de Aledo, P.G.: Skink: static analysis of programs in LLVM intermediate representation - (Competition Contribution). In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10206, pp. 380–384. Springer, Heidelberg (2017). doi:10.1007/978-3-662-54580-5_27 CrossRefGoogle Scholar
  12. 12.
    Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000). doi:10.1007/10722167_15 CrossRefGoogle Scholar
  13. 13.
    Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78800-3_24 CrossRefGoogle Scholar
  14. 14.
    Dierks, H., Kupferschmid, S., Larsen, K.G.: Automatic abstraction refinement for timed automata. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 114–129. Springer, Heidelberg (2007). doi:10.1007/978-3-540-75454-1_10 CrossRefGoogle Scholar
  15. 15.
    Frehse, G.: PHAVer: algorithmic verification of hybrid systems past HyTech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31954-2_17 CrossRefGoogle Scholar
  16. 16.
    Frehse, G., Guernic, C., Donzé, A., Cotton, S., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: SpaceEx: scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22110-1_30 CrossRefGoogle Scholar
  17. 17.
    Heizmann, M., Hoenicke, J., Podelski, A.: Refinement of trace abstraction. In: Palsberg, J., Su, Z. (eds.) SAS 2009. LNCS, vol. 5673, pp. 69–85. Springer, Heidelberg (2009). doi:10.1007/978-3-642-03237-0_7 CrossRefGoogle Scholar
  18. 18.
    Heizmann, M., Hoenicke, J., Podelski, A.: Software model checking for people who love automata. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 36–52. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39799-8_2 CrossRefGoogle Scholar
  19. 19.
    Henzinger, T.A., Ho, P.-H., Wong-toi, H.: HyTech: a model checker for hybrid systems. Softw. Tools Technol. Transf. 1, 460–463 (1997)MATHGoogle Scholar
  20. 20.
    Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? J. Comput. Syst. Sci. 57(1), 94–124 (1998)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Kordy, P., Langerak, R., Mauw, S., Polderman, J.W.: A symbolic algorithm for the analysis of robust timed automata. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 351–366. Springer, Cham (2014). doi:10.1007/978-3-319-06410-9_25 CrossRefGoogle Scholar
  22. 22.
    Sankur, O.: Symbolic quantitative robustness analysis of timed automata. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 484–498. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46681-0_48 Google Scholar
  23. 23.
    Wang, W., Jiao, L.: Trace abstraction refinement for timed automata. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 396–410. Springer, Cham (2014). doi:10.1007/978-3-319-11936-6_28 Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Franck Cassez
    • 1
  • Peter Gjøl Jensen
    • 1
    • 2
  • Kim Guldstrand Larsen
    • 2
  1. 1.Department of ComputingMacquarie UniversitySydneyAustralia
  2. 2.Department of Computer ScienceAalborg UniversityAalborgDenmark

Personalised recommendations