Advertisement

The Power of Proofs: New Algorithms for Timed Automata Model Checking

  • Peter Fontana
  • Rance Cleaveland
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8711)

Abstract

This paper presents the first model-checking algorithm for an expressive modal mu-calculus over timed automata, \(L^{\mathit{rel}, \mathit{af}}_{\nu,\mu}\), and reports performance results for an implementation. This mu-calculus contains extended time-modality operators and can express all of TCTL. Our algorithmic approach uses an “on-the-fly” strategy based on proof search as a means of ensuring high performance for both positive and negative answers to model-checking questions. In particular, a set of proof rules for solving model-checking problems are given and proved sound and complete; our algorithm then model-checks a property by constructing a proof (or showing none exists) using these rules. One noteworthy aspect of our technique is that we show that verification performance can be improved with derived rules, whose correctness can be inferred from the more primitive rules on which they are based. In this paper, we give the basic proof rules underlying our method, describe derived proof rules to improve performance, and we compare our implementation to UPPAAL.

Keywords

Model Check Atomic Proposition Time Advance Liveness Property Proof Rule 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aceto, L., Laroussinie, F.: Is your model checker on time? on the complexity of model checking for timed modal logics. Journal of Logic and Algebraic Programming 52-53, 7–51 (2002)Google Scholar
  2. 2.
    Alur, R.: Timed Automata. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 8–22. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  3. 3.
    Alur, R., Courcoubetis, C., Dill, D.: Model-checking in dense real-time. Information and Computation 104(1), 2–34 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Behrmann, G., Larsen, K.G., Pearson, J., Weise, C., Yi, W.: Efficient Timed Reachability Analysis Using Clock Difference Diagrams. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 341–353. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Bouyer, P., Cassez, F., Laroussinie, F.: Timed modal logics for real-time systems. Journal of Logic, Language and Information 20(2), 169–203 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Bowman, H., Gomez, R.: How to stop time stopping. Formal Aspects of Computing 18(4), 459–493 (2006)CrossRefzbMATHGoogle Scholar
  9. 9.
    Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. TOPLAS 8(2), 244–263 (1986)CrossRefzbMATHGoogle Scholar
  10. 10.
    Cleaveland, R.: Tableau-Based Model Checking in the Propositional Mu-Calculus. Acta Informatica 27(9), 725–747 (1990)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Cleaveland, R., Steffen, B.: A Linear-Time Model-Checking Algorithm for the Alternation-Free Modal Mu-Calculus. Formal Methods in System Design 2(2), 121–147 (1993)CrossRefzbMATHGoogle Scholar
  12. 12.
    Emerson, E.A., Lei, C.L.: Efficient Model Checking in Fragments of the Propositional Mu-Calculus. In: LICS 1986, pp. 267–278. IEEE Computer Society (1986)Google Scholar
  13. 13.
    Fontana, P., Cleaveland, R.: Data Structure Choices for On-the-Fly Model Checking of Real-Time Systems. In: DIFTS 2011, pp. 13–21 (2011)Google Scholar
  14. 14.
    Fontana, P., Cleaveland, R.: Expressiveness results for timed modal-mu calculi (2014) (in Preparation Preprint available upon request)Google Scholar
  15. 15.
    Fontana, P., Cleaveland, R.: A menagerie of timed automata. ACM Computing Surveys 46(3), 40:1–40:56 (2014)Google Scholar
  16. 16.
    Fontana, P., Cleaveland, R.: The power of proofs: New algorithms for timed automata model checking (appendix). arXiv.org (2014)Google Scholar
  17. 17.
    Heitmeyer, C., Lynch, N.: The generalized railroad crossing: a case study in formal verification of real-time systems. In: RTSS 1994, pp. 120–131 (December 1994)Google Scholar
  18. 18.
    Henzinger, T., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model checking for real-time systems. Information and Computation 111(2), 193–244 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Laroussinie, F., Larsen, K.G.: CMC: A tool for compositional model-checking of real-time systems. In: Budkowski, S., Cavalli, A., Najm, E. (eds.) Formal Description Techniques and Protocol Specification, Testing and Verification. IFIP, pp. 439–456. Springer, US (1998)Google Scholar
  20. 20.
    Peter, H.J., Ehlers, R., Mattmüller, R.: Synthia: Verification and synthesis for timed automata. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 649–655. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  21. 21.
    Sokolsky, O.V., Smolka, S.A.: Local model checking for real-time systems. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 211–224. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  22. 22.
    Wang, F.: Efficient verification of timed automata with BDD-like data structures. STTT 6(1), 77–97 (2004)CrossRefGoogle Scholar
  23. 23.
    Wang, F.: Redlib for the formal verification of embedded systems. In: ISoLA 2006, pp. 341–346. IEEE Computer Society, Piscataway (2006)Google Scholar
  24. 24.
    Wang, F., Huang, G.D., Yu, F.: TCTL inevitability analysis of dense-time systems: From theory to engineering. IEEE Transactions on Software Engineering 32(7), 510–526 (2006)CrossRefGoogle Scholar
  25. 25.
    Yovine, S.: KRONOS: a verification tool for real-time systems. STTT 1(1), 123–133 (1997)CrossRefzbMATHGoogle Scholar
  26. 26.
    Zhang, D., Cleaveland, W.R.: Fast generic model-checking for data-based systems. In: Wang, F. (ed.) FORTE 2005. LNCS, vol. 3731, pp. 83–97. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  27. 27.
    Zhang, D., Cleaveland, R.: Fast on-the-fly parametric real-time model checking. In: RTSS 2005, pp. 157–166. IEEE Computer Society, Washington, DC (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Peter Fontana
    • 1
  • Rance Cleaveland
    • 1
  1. 1.Department of Computer ScienceUniversity of MarylandCollege ParkUSA

Personalised recommendations