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
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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)
Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)
Alur, R., Feder, T., Henzinger, T.: The benefits of relaxing punctuality. Journal of the ACM 43(1), 116–146 (1996)
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)
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)
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)
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)
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)
Bérard, B., Dufourd, C.: Timed automata and additive clock constraints. Information Processing Letters 75(1-2), 1–7 (2000)
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)
Bouyer, P.: Forward analysis of updatable timed automata. Formal Methods in System Design 24(3), 281–320 (2004)
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)
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)
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)
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)
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)
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)
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)
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)
Gupta, V., Henzinger, T., Jagadeesan, R.: Robust timed automata. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 48–62. Springer, Heidelberg (1997)
Henzinger, T., Kopke, P., Puri, A., Varaiya, P.: What’s decidable about hybrid automata. Journal of Computer and System Sciences 57, 94–124 (1998)
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)
Henzinger, T., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model-checking for real-time systems. Information and Computation 111(2), 193–244 (1994)
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)
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)
Herrmann, P.: Timed automata and recognizability. Information Processing Letters 65(6), 313–318 (1998)
La Torre, S., Mukhopadhyay, S., Alur, R.: Subclasses of timed automata with NP-complete reachability problem. Technical report (2003) (unpublished)
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)
Larsen, K., Pettersson, P., Yi, W.: Uppaal in a nutshell. Springer International Journal of Software Tools for Technology Transfer 1 (1997)
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)
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)
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)
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)
Raskin, J., Schobbens, P.: The logic of event clocks – decidability, complexity, and expressiveness. Journal of Automata, Languages, and Combinatorics 4(3), 247–286 (1999)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-540-30080-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23068-7
Online ISBN: 978-3-540-30080-9
eBook Packages: Springer Book Archive