Real Time Temporal Logic: Past, Present, Future

  • Oded Maler
  • Dejan Nickovic
  • Amir Pnueli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3829)


This paper attempts to improve our understanding of timed languages and their relation to timed automata. We start by giving a constructive proof of the folk theorem stating that timed languages specified by the past fragment of mitl, can be accepted by deterministic timed automata. On the other hand we provide a proof that certain languages expressed in the future fragment of mitl are not deterministic, and analyze the reason for this asymmetry.


Temporal Logic Acceptance Condition Semantic Domain Time Automaton Deterministic Automaton 
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.


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  1. Alur, R.: Timed Automata. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 8–22. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  2. Alur, R., Dill, D.L.: A Theory of Timed Automata. Theoretical Computer Science 126, 183–235 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  3. Alur, R., Feder, T., Henzinger, T.A.: The Benefits of Relaxing Punctuality. Journal of the ACM 43(1), 116–146 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  4. Alur, R., Fix, L., Henzinger, T.A.: Event-Clock Automata: A Determinizable Class of Timed Automata. Theoretical Computer Science 211, 253–273 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  5. Alur, R., Henzinger, T.A.: Logics and Models of Real-Time: A Survey. In: Huizing, C., de Bakker, J.W., Rozenberg, G., de Roever, W.-P. (eds.) REX 1991. LNCS, vol. 600, pp. 74–106. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  6. Alur, R., Henzinger, T.A.: Back to the Future: Towards a Theory of Timed Regular Languages. In: Proc. FOCS 1992, pp. 177–186 (1992)Google Scholar
  7. Asarin, E.: Challenges in Timed Languages. Bulletin of EATCS, vol. 83 (2004)Google Scholar
  8. Asarin, E., Caspi, P., Maler, O.: Timed Regular Expressions. The Journal of the ACM 49, 172–206 (2002)CrossRefMathSciNetGoogle Scholar
  9. Daws, C., Yovine, S.: Reducing the Number of Clock Variables of Timed Automata. In: Proc. RTSS 1996, pp. 73–81. IEEE, Los Alamitos (1996)Google Scholar
  10. Eisner, C., Fisman, D., Havlicek, J., Lustig, Y., McIsaac, A., Van Campenhout, D.: Reasoning with Temporal Logic on Truncated Paths. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 27–39. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. Geilen, M.C.W.: Formal Techniques for Verification of Complex Real-time Systems. PhD thesis, Eindhoven University of Technology (2002)Google Scholar
  12. 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
  13. Havelund, K., Rosu, G.: Synthesizing Monitors for Safety Properties. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 342–356. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. Henzinger, T., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic Model-checking for Real-time Systems. Information and Computation 111, 193–244 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  15. Hirshfeld, Y., Rabinovich, A.: Logics for Real Time: Decidability and Complexity. Fundamenta Informaticae 62, 1–28 (2004)zbMATHMathSciNetGoogle Scholar
  16. Koymans, R.: Specifying Real-time Properties with with Metric Temporal Logic. Real-time Systems, pp. 255–299 (1990)Google Scholar
  17. Kristoffersen, K.J., Pedersen, C., Andersen, H.R.: Runtime Verification of Timed LTL using Disjunctive Normalized Equation Systems. In: Proc. RV 2003. ENTCS, vol. 89(2) (2003)Google Scholar
  18. Krichen, M., Tripakis, S.: Black-box Conformance Testing for Real-time Systems. In: Graf, S., Mounier, L. (eds.) SPIN 2004. LNCS, vol. 2989, pp. 109–126. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. Lichtenstein, O., Pnueli, A., Zuck, L.D.: The Glory of the Past. In: Parikh, R. (ed.) Logic of Programs 1985. LNCS, vol. 193, pp. 196–218. Springer, Heidelberg (1985)Google Scholar
  20. Lasota, S., Walukiewicz, L.: Alternating Timed Automata. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 250–265. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  21. Maler, O., Nickovic, D.: Monitoring Temporal Properties of Continuous Signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253. Springer, Heidelberg (2004)Google Scholar
  22. Maler, O., Pnueli, A.: Tight Bounds on the Complexity of Cascaded Decomposition of Automata. In: Proc. FOCS 1990, pp. 672–682 (1990)Google Scholar
  23. Maler, O., Pnueli, A.: Timing Analysis of Asynchronous Circuits using Timed Automata. In: Camurati, P.E., Eveking, H. (eds.) CHARME 1995. LNCS, vol. 987, pp. 189–205. Springer, Heidelberg (1995)Google Scholar
  24. Maler, O., Pnueli, A.: On Recognizable Timed Languages. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 348–362. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  25. Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems: Safety. Springer, Heidelberg (1995)Google Scholar
  26. McNaughton, R., Papert, S.: Counter Free Automata. MIT Press, Cambridge (1971)zbMATHGoogle Scholar
  27. Nivat, M., Perrin, D.: Ensembles Reconnaissables de Mots Bi-infinis. Canadian J. of Mathematics 38, 513–537 (1986)zbMATHMathSciNetCrossRefGoogle Scholar
  28. Ouaknine, J., Worrell, J.: On the Decidability of Metric Temporal Logic. In: Proc. LICS 2005 (2005) (to appear)Google Scholar
  29. Pnueli, A.: Verification of Reactive Systems. Lecture Notes, NYU (2003),
  30. Raskin, J.-F., Schobbens, P.Y., Henzinger, T.A.: Axioms for Real-Time Logics. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 219–236. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  31. Safra, S.: On the Complexity of ω-automata. In: Proc. FOCS 1988, pp. 319–327 (1998)Google Scholar
  32. Springintveld, J.G., Vaandrager, F.W.: Minimizable Timed Automata. In: Jonsson, B., Parrow, J. (eds.) FTRTFT 1996. LNCS, vol. 1135, pp. 130–147. Springer, Heidelberg (1996)Google Scholar
  33. Thati, P., Rosu, G.: Monitoring Algorithms for Metric Temporal Logic Specifications. In: Proc. of RV 2004 (2004)Google Scholar
  34. Tripakis, S.: Fault Diagnosis for Timed Automata. In: Damm, W., Olderog, E.-R. (eds.) FTRTFT 2002. LNCS, vol. 2469, pp. 205–224. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  35. Vardi, M.Y., Wolper, P.: An Automata-theoretic Approach to Automatic Program Verification. In: Proc. LICS 1986, pp. 322–331. IEEE, Los Alamitos (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Oded Maler
    • 1
  • Dejan Nickovic
    • 1
  • Amir Pnueli
    • 2
    • 3
  1. 1.VerimagGièresFrance
  2. 2.Weizmann Institute of ScienceRehovotIsrael
  3. 3.New York UniversityNew YorkUSA

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