Hierarchical Reasoning for the Verification of Parametric Systems

  • Viorica Sofronie-Stokkermans
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6173)


We study certain classes of verification problems for parametric reactive and hybrid systems, and identify the types of logical theories which can be used for modeling such systems and the reasoning tasks which need to be solved in this context. We identify properties of the underlying theories which ensure that these classes of verification problems can be solved efficiently, give examples of theories with the desired properties, and illustrate the methods we use on several examples.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alur, R., Henzinger, T.A., Ho, P.H.: Automatic Symbolic Verification of Embedded Systems. IEEE Trans. Software Eng. 22(3), 181–201 (1996)CrossRefGoogle Scholar
  2. 2.
    Beyer, D., Henzinger, T., Majumdar, R., Rybalchenko, A.: Invariant Synthesis for Combined Theories. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 378–394. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Cimatti, A., Palopoli, L., Ramadian, Y.: Symbolic Computation of Schedulability Regions Using Parametric Timed Automata. In: IEEE Real-Time Systems Symposium 2008, pp. 80–89. IEEE Computer Society, Los Alamitos (2008)CrossRefGoogle Scholar
  4. 4.
    Cimatti, A., Roveri, M., Tonetta, S.: Requirements Validation for Hybrid Systems. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 188–203. Springer, Heidelberg (2009)Google Scholar
  5. 5.
    Dolzmann, A., Sturm, T.: Redlog: Computer Algebra Meets Computer Logic. ACM SIGSAM Bulletin 31(2), 2–9 (1997)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Frehse, G., Jha, S.K., Krogh, B.H.: A Counterexample-Guided Approach to Parameter Synthesis for Linear Hybrid Automata. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 187–200. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Ganzinger, H., Sofronie-Stokkermans, V., Waldmann, U.: Modular proof systems for partial functions with Evans equality. Information and Computation 204(10), 1453–1492 (2006)CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Ghilardi, S., Nicolini, E., Ranise, S., Zucchelli, D.: Combination Methods for Satisfiability and Model-Checking of Infinite-State Systems. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 362–378. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Gulwani, S., Tiwari, A.: Constraint-Based Approach for Analysis of Hybrid Systems. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 190–203. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Hune, T., Romijn, J., Stoelinga, M., Vaandrager, F.: Linear Parametric Model Checking of Timed Automata. Journal of Logic and Algebraic Programming 52-53, 183–220 (2002)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Ihlemann, C., Jacobs, S., Sofronie-Stokkermans, V.: On Local Reasoning in Verification. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 265–281. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Ihlemann, C., Sofronie-Stokkermans, V.: On Hierarchical Reasoning in Combinations of Theories. In: Giesl, J., Hähnle, R. (eds.) Proceedings of IJCAR 2010. LNCS (LNAI), vol. 6173, pp. 30–45. Springer, Heidelberg (2010)Google Scholar
  13. 13.
    Jacobs, S., Sofronie-Stokkermans, V.: Applications of Hierarchical Reasoning in the Verification of Complex Systems. Electr. Notes Theor. Comput. Sci. 174(8), 39–54 (2007)CrossRefGoogle Scholar
  14. 14.
    Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems: Safety. Springer, Heidelberg (1995)Google Scholar
  15. 15.
    Platzer, A., Quesel, J.-D.: European Train Control System: A Case Study in Formal Verification. In: Cavalcanti, A. (ed.) ICFEM 2009. LNCS, vol. 5885, pp. 246–265. Springer, Heidelberg (2009)Google Scholar
  16. 16.
    Sofronie-Stokkermans, V.: Hierarchic Reasoning in Local Theory Extensions. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 219–234. Springer, Heidelberg (2005)Google Scholar
  17. 17.
    Sofronie-Stokkermans, V., Ihlemann, C.: Automated Reasoning in some Local Extensions of Ordered Structures. Journal of Multiple-Valued Logics and Soft Computing 13(4-6), 397–414 (2007)MathSciNetMATHGoogle Scholar
  18. 18.
    Sofronie-Stokkermans, V.: Efficient Hierarchical Reasoning about Functions over Numerical Domains. In: Dengel, A.R., Berns, K., Breuel, T.M., Bomarius, F., Roth-Berghofer, T.R. (eds.) KI 2008. LNCS (LNAI), vol. 5243, pp. 135–143. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Tarski, A.: A Decision Method for Elementary Algebra and Geometry, 2nd edn. University of California Press, Berkeley (1951)MATHGoogle Scholar
  20. 20.
    Wang, F.: Symbolic Parametric Safety Analysis of Linear Hybrid Systems with BDD-Like Data-Structures. IEEE Trans. Software Eng. 31(1), 38–51 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Viorica Sofronie-Stokkermans
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

Personalised recommendations