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LTL Parameter Synthesis of Parametric Timed Automata

  • Peter Bezděk
  • Nikola Beneš
  • Jiří Barnat
  • Ivana Černá
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9763)

Abstract

The parameter synthesis problem for parametric timed automata is undecidable in general even for very simple reachability properties. In this paper we introduce restrictions on parameter valuations under which the parameter synthesis problem is decidable for LTL properties. The investigated bounded integer parameter synthesis problem could be solved using an explicit enumeration of all possible parameter valuations. We propose an alternative symbolic zone-based method for this problem which results in a faster computation. Our technique extends the ideas of the automata-based approach to LTL model checking of timed automata. To justify the usefulness of our approach, we provide experimental evaluation and compare our method with explicit enumeration technique.

Keywords

Linear Time Logic Linear Time Logic Formula Parameter Valuation Reachability Property Explicit Enumeration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  2. 2.
    Alur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126(2), 183–235 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Daws, C., Tripakis, S.: Model checking of real-time reachability properties using abstractions. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 313–329. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  4. 4.
    Behrmann, G., David, A., Larsen, K.G., Hakansson, J., Petterson, P., Yi, W., Hendriks, M.: Uppaal 4.0. In: QEST, pp. 125–126. IEEE (2006)Google Scholar
  5. 5.
    Alur, R., Henzinger, T.A., Vardi, M.Y.: Parametric real-time reasoning. In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, pp. 592–601. ACM (1993)Google Scholar
  6. 6.
    Miller, J.S.: 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, p. 296. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Beneš, N., Bezděk, P., Larsen, K.G., Srba, J.: Language emptiness of continuous-time parametric timed automata. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 69–81. Springer, Heidelberg (2015)Google Scholar
  8. 8.
    Hune, T., Romijn, J., Stoelinga, M., Vaandrager, F.: Linear parametric model checking of timed automata. J. Logic Algebraic Programm. 52, 183–220 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Bozzelli, L., La Torre, S.: Decision problems for lower/upper bound parametric timed automata. Formal Methods Syst. Des. 35(2), 121–151 (2009)CrossRefzbMATHGoogle Scholar
  10. 10.
    Jovanovic, A., Lime, D., Roux, O.H.: Integer parameter synthesis for real-time systems. IEEE Trans. Softw. Eng. 41(5), 445–461 (2015)CrossRefGoogle Scholar
  11. 11.
    Tripakis, S., Yovine, S., Bouajjani, A.: Checking timed büchi automata emptiness efficiently. Formal Methods Syst. Des. 26(3), 267–292 (2005)CrossRefzbMATHGoogle Scholar
  12. 12.
    Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) Automatic Verification Methods for Finite State Systems. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  13. 13.
    Bouyer, P.: Forward analysis of updatable timed automata. Formal Methods Syst. Des. 24(3), 281–320 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Behrmann, G., Bouyer, P., Larsen, K.G., Pelánek, R.: Lower and upper bounds in zone-based abstractions of timed automata. Int. J. Softw. Tools Technol. Transf. 8(3), 204–215 (2006)CrossRefzbMATHGoogle Scholar
  15. 15.
    Li, G.: Checking timed Büchi automata emptiness using LU-abstractions. In: Ouaknine, J., Vaandrager, F.W. (eds.) FORMATS 2009. LNCS, vol. 5813, pp. 228–242. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Bezděk, P., Beneš, N., Barnat, J., Černá, I.: LTL parameter synthesis of parametric timed automata. CoRR abs/1409.3696 (2016)Google Scholar
  17. 17.
    Courcoubetis, C., Vardi, M., Wolper, P., Yannakakis, M.: Memory-efficient algorithms for the verification of temporal properties. In: Clarke, E.M., Kurshan, R.P. (eds.) CAV. LNCS, vol. 531, pp. 233–242. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  18. 18.
    Bagnara, R., Hill, P.M., Zaffanella, E.: The parma polyhedra library: toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Sci. Comput. Programm. 72(1–2), 3–21 (2008)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Gastin, P., Oddoux, D.: Fast LTL to Büchi automata translation. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, p. 53. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  20. 20.
    Behrmann, G., David, A., Larsen, K.G.: A tutorial on Uppaal. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 200–236. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  21. 21.
    Bezděk, P., Beneš, N., Havel, V., Barnat, J., Černá, I.: On clock-aware LTL properties of timed automata. In: Ciobanu, G., Méry, D. (eds.) ICTAC 2014. LNCS, vol. 8687, pp. 43–60. Springer, Heidelberg (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Peter Bezděk
    • 1
  • Nikola Beneš
    • 1
  • Jiří Barnat
    • 1
  • Ivana Černá
    • 1
  1. 1.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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