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Formal Methods for the Design of Real-Time Systems

SFM-RT 2004: Formal Methods for the Design of Real-Time Systems pp 1–24Cite as

Decision Problems for Timed Automata: A Survey

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 3185)

Abstract

Finite automata and regular languages have been useful in a wide variety of problems in computing, communication and control, including formal modeling and verification. Traditional automata do not admit an explicit modeling of time, and consequently, timed automata [2] were introduced as a formal notation to model the behavior of real-time systems. Timed automata accept timed languages consisting of sequences of events tagged with their occurrence times. Over the years, the formalism has been extensively studied leading to many results establishing connections to circuits and logic, and much progress has been made in developing verification algorithms, heuristics, and tools. This paper provides a survey of the theoretical results concerning decision problems of reachability, language inclusion and language equivalence for timed automata and its variants, with some new proofs and comparisons. We conclude with a discussion of some open problems.

Keywords

  • Regular Language
  • Hybrid Automaton
  • Reachability Problem
  • Time Automaton
  • 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.

This research was partially supported by NSF award ITR/SY 0121431.

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References

  1. Alur, R., Courcoubetis, C., Henzinger, T.: The observational power of clocks. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 162–177. Springer, Heidelberg (1994)

    CrossRef  Google Scholar 

  2. Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)

    MATH  CrossRef  MathSciNet  Google Scholar 

  3. Alur, R., Feder, T., Henzinger, T.: The benefits of relaxing punctuality. Journal of the ACM 43(1), 116–146 (1996)

    MATH  CrossRef  MathSciNet  Google Scholar 

  4. Alur, R., Fix, L., Henzinger, T.: Event-clock automata: a determinizable class of timed automata. Theoretical Computer Science 211, 253–273, (1999); A preliminary version Dill, D.L. (ed.): CAV 1994. LNCS, vol. 818, pp. 1–13. Springer, Heidelberg (1994)

    MATH  Google Scholar 

  5. Alur, R., Henzinger, T.: Back to the future: Towards a theory of timed regular languages. In: Proceedings of the 33rd IEEE Symposium on Foundations of Computer Science, pp. 177–186 (1992)

    Google Scholar 

  6. Alur, R., Kurshan, R.: Timing analysis in COSPAN. In: Alur, R., Sontag, E.D., Henzinger, T.A. (eds.) HS 1995. LNCS, vol. 1066, pp. 220–231. Springer, Heidelberg (1996)

    CrossRef  Google Scholar 

  7. Alur, R., La Torre, S., Pappas, G.: Optimal paths in weighted timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 49–62. Springer, Heidelberg (2001)

    CrossRef  Google Scholar 

  8. Behrman, G., Hune, T., Fehnker, A., Larsen, K., Petersson, P., Romijn, J., Vaandrager, F.: Minimum-cost reachability for priced timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 147–161. Springer, Heidelberg (2001)

    CrossRef  Google Scholar 

  9. Bérard, B., Dufourd, C.: Timed automata and additive clock constraints. Information Processing Letters 75(1-2), 1–7 (2000)

    MATH  CrossRef  MathSciNet  Google Scholar 

  10. Berard, B., Gastin, P., Petit, A.: On the power of non-obervable actions in timed automata. In: Puech, C., Reischuk, R. (eds.) STACS 1996. LNCS, vol. 1046, pp. 257–268. Springer, Heidelberg (1996)

    Google Scholar 

  11. Bouyer, P.: Forward analysis of updatable timed automata. Formal Methods in System Design 24(3), 281–320 (2004)

    MATH  CrossRef  Google Scholar 

  12. Bouyer, P., Brinksma, E., Larsen, K.: Staying alive as cheaply as possible. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 203–218. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  13. Bouyer, P., Dufourd, C., Fleury, E., Petit, A.: Are timed automata updatable? In: Computer Aided Verification, 14th International Conference. LNCS, vol. 2404, pp. 464–479 (2000)

    Google Scholar 

  14. Cassez, F., Henzinger, T., Raskin, J.: A comparison of control problems for timed and hybrid systems. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, pp. 134–148. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  15. Courcoubetis, C., Yannakakis, M.: Minimum and maximum delay problems in real-time systems. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575, pp. 399–409. Springer, Heidelberg (1992)

    Google Scholar 

  16. Daws, C., Olivero, A., Tripakis, S., Yovine, S.: The tool kronos. In: Alur, R., Sontag, E.D., Henzinger, T.A. (eds.) HS 1995. LNCS, vol. 1066, pp. 208–219. Springer, Heidelberg (1996)

    CrossRef  Google Scholar 

  17. DeWulf, M., Doyen, L., Markey, N., Raskin, J.: Robustness and implementability of timed automata. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 118–133. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  18. D’Souza, D.: A logical characterisation of event recording automata. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, pp. 240–251. Springer, Heidelberg (2000)

    CrossRef  Google Scholar 

  19. D’Souza, D., Madhusudan, P.: Timed control synthesis for external specifications. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 571–582. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  20. Gupta, V., Henzinger, T., Jagadeesan, R.: Robust timed automata. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 48–62. Springer, Heidelberg (1997)

    CrossRef  Google Scholar 

  21. Henzinger, T., Kopke, P., Puri, A., Varaiya, P.: What’s decidable about hybrid automata. Journal of Computer and System Sciences 57, 94–124 (1998)

    MATH  CrossRef  MathSciNet  Google Scholar 

  22. Henzinger, T., Manna, Z., Pnueli, A.: What good are digital clocks? In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 545–558. Springer, Heidelberg (1992)

    Google Scholar 

  23. Henzinger, T., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model-checking for real-time systems. Information and Computation 111(2), 193–244 (1994)

    MATH  CrossRef  MathSciNet  Google Scholar 

  24. Henzinger, T., Raskin, J.: Robust undecidability of timed and hybrid systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 145–159. Springer, Heidelberg (2000)

    CrossRef  Google Scholar 

  25. Henzinger, T., Raskin, J., Schobbens, P.: The regular real-time languages. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 580–593. Springer, Heidelberg (1998)

    CrossRef  Google Scholar 

  26. Herrmann, P.: Timed automata and recognizability. Information Processing Letters 65(6), 313–318 (1998)

    MATH  CrossRef  MathSciNet  Google Scholar 

  27. La Torre, S., Mukhopadhyay, S., Alur, R.: Subclasses of timed automata with NP-complete reachability problem. Technical report (2003) (unpublished)

    Google Scholar 

  28. Laroussinie, F., Markey, N., Schnoebelen, P.: Model checking timed automata with one or two clocks. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 387–401. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  29. Larsen, K., Pettersson, P., Yi, W.: Uppaal in a nutshell. Springer International Journal of Software Tools for Technology Transfer 1 (1997)

    Google Scholar 

  30. Miller, J.: 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, pp. 296–309. Springer, Heidelberg (2000)

    CrossRef  Google Scholar 

  31. Ouaknine, J., Worrell, J.: Revisiting digitization, robustness, and decidability for timed automata. In: Proceedings of the 18th IEEE Symposium on Logic in Computer Science (2003)

    Google Scholar 

  32. Ouaknine, J., Worrell, J.: On the language inclusion problem for timed automata: Closing a decidability gap. In: Proceedings of the 19th IEEE Symposium on Logic in Computer Science (2004)

    Google Scholar 

  33. Puri, A.: Dynamical properties of timed automata. In: Ravn, A.P., Rischel, H. (eds.) FTRTFT 1998. LNCS, vol. 1486, pp. 210–227. Springer, Heidelberg (1998)

    CrossRef  Google Scholar 

  34. Raskin, J., Schobbens, P.: The logic of event clocks – decidability, complexity, and expressiveness. Journal of Automata, Languages, and Combinatorics 4(3), 247–286 (1999)

    MATH  MathSciNet  Google Scholar 

  35. Tripakis, S.: Folk theorems on determinization and minimization of timed automata. In: Larsen, K.G., Niebert, P. (eds.) FORMATS 2003. LNCS, vol. 2791, Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  36. Wang, F.: Efficient data structures for fully symbolic verification of real-time software systems. In: Schwartzbach, M.I., Graf, S. (eds.) TACAS 2000. LNCS, vol. 1785, pp. 157–171. Springer, Heidelberg (2000)

    CrossRef  Google Scholar 

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Authors and Affiliations

  1. University of Pennsylvania,  

    Rajeev Alur & P. Madhusudan

Authors
  1. Rajeev Alur
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  2. P. Madhusudan
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Editors and Affiliations

  1. Istituto di Scienze e Tecnologie dell’Informazione, Università di Urbino “Carlo Bo”, Italy

    Marco Bernardo

  2. Dipartimento di Matematica ed Informatica, University of Camerino, Via Madonna delle Carceri 9, 62032, Camerino, Italy

    Flavio Corradini

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Alur, R., Madhusudan, P. (2004). Decision Problems for Timed Automata: A Survey. In: Bernardo, M., Corradini, F. (eds) Formal Methods for the Design of Real-Time Systems. SFM-RT 2004. Lecture Notes in Computer Science, vol 3185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30080-9_1

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  • DOI: https://doi.org/10.1007/978-3-540-30080-9_1

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