Advertisement

Abstract

Metric Temporal Logic (MTL) is a widely-studied real-time extension of Linear Temporal Logic. In this paper we consider a fragment of MTL, called Safety MTL, capable of expressing properties such as invariance and time-bounded response. Our main result is that the satisfiability problem for Safety MTL is decidable. This is the first positive decidability result for MTL over timed ω-words that does not involve restricting the precision of the timing constraints, or the granularity of the semantics; the proof heavily uses the techniques of infinite-state verification. Combining this result with some of our previous work, we conclude that Safety MTL is fully decidable in that its satisfiability, model checking, and refinement problems are all decidable.

Keywords

Model Check Temporal Logic Linear Temporal Logic Extra Delay Clock Constraint 
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.
    Abdulla, P.A., Deneux, J., Ouaknine, J., Worrell, J.B.: Decidability and complexity results for timed automata via channel machines. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1089–1101. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Abdulla, P.A., Jonsson, B.: Undecidable verification problems with unreliable channels. Information and Computation 130, 71–90 (1996)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Abdulla, P.A., Jonsson, B.: Model checking of systems with many identical timed processes. Theoretical Computer Science 290(1), 241–264 (2003)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. Journal of the ACM 43, 116–146 (1996)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Alur, R., Henzinger, T.A.: Real-time logics: complexity and expressiveness. Information and Computation 104, 35–77 (1993)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Alur, R., Henzinger, T.A.: A really temporal logic. Journal of the ACM 41, 181–204 (1994)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Bouyer, P., Chevalier, F., Markey, N.: On the expressiveness of TPTL and MTL. Research report LSV-2005-05, Lab. Spécification et Vérification (May 2005)Google Scholar
  9. 9.
    Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theoretical Computer Science 256(1-2), 63–92 (2001)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Henzinger, T.A.: It’s about time: Real-time logics reviewed. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 439–454. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    Henzinger, T.A., Manna, Z., Pnueli, A.: What good are digital clocks? In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623. Springer, Heidelberg (1992)Google Scholar
  12. 12.
    Henzinger, T.A., Raskin, J.-F., Schobbens, P.-Y.: The regular real-time languages. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, p. 580. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. 13.
    Higman, G.: Ordering by divisibility in abstract algebras. Proceedings of the London Mathematical Society 2, 236–366 (1952)MathSciNetMATHGoogle Scholar
  14. 14.
    Koymans, R.: Specifying real-time properties with metric temporal logic. Real-time Systems 2(4), 255–299 (1990)CrossRefGoogle Scholar
  15. 15.
    Lasota, S., Walukiewicz, I.: Alternating timed automata. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 250–265. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Ouaknine, J., Worrell, J.: On the decidability of Metric Temporal Logic. In: Proceedings of LICS 2005. IEEE Computer Society Press, Los Alamitos (2005)Google Scholar
  17. 17.
    Ouaknine, J., Worrell, J.: Metric temporal logic and faulty Turing machines. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006. LNCS, vol. 3921, p. 447. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. 18.
    Ouaknine, J., Worrell, J.: Safety MTL is fully decidable. Oxford University Programming Research Group Research Report RR-06-02Google Scholar
  19. 19.
    Raskin, J.-F., Schobbens, P.-Y.: State-clock logic: a decidable real-time logic. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, p. 417. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  20. 20.
    Vardi, M.: Alternating automata: Unifying truth and validity checking for temporal logics. In: McCune, W. (ed.) CADE 1997. LNCS, vol. 1249. Springer, Heidelberg (1997)Google Scholar
  21. 21.
    Wang, F.: Formal Verification of Timed Systems: A Survey and Perspective. Proceedings of the IEEE 92(8), 1283–1307 (2004)CrossRefGoogle Scholar
  22. 22.
    Wilke, T.: Specifying timed state sequences in powerful decidable logics and timed automata. In: Langmaack, H., de Roever, W.-P., Vytopil, J. (eds.) FTRTFT 1994 and ProCoS 1994. LNCS, vol. 863, p. 787. Springer, Heidelberg (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Joël Ouaknine
    • 1
  • James Worrell
    • 1
  1. 1.Oxford University Computing LaboratoryUK

Personalised recommendations