Abstract
We give a new discretization of behaviors of timed automata. In this discretization, timed languages are represented as sets of words containing action symbols, a clock tick symbol 1, and two delay symbols δ − (negative delay) and δ + (positive delay). Unlike the region construction, our discretization commutes with intersection. We show that discretizations of timed automata are, in general, context-sensitive languages over Σ ∪ {1,δ + ,δ −, and give a class of automata that equals the class of languages that are discretizations of timed automata, and show that their emptiness problem is decidable.
This work has been partially supported by the Action Spécifique STIC-CNRS no. 93 “Automates Distribués et Temporisés”
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
Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. Journal of ACM 49, 172–206 (2002)
Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)
Asarin, E., Dima, C.: Balanced timed regular expressions. ENTCS, vol. 68(5) (2003)
Beauquier, D.: Pumping lemmas for timed automata. In: Nivat, M. (ed.) FOSSACS 1998. LNCS, vol. 1378, pp. 81–94. Springer, Heidelberg (1998)
Bellmann, R.: Dynamic Programming. Princeton University Press, Princeton (1957)
Bouyer, P., Petit, A.: Decomposition and composition of timed automata. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 210–219. Springer, Heidelberg (1999)
Bouyer, P., Petit, A.: A Kleene/Büchi-like theorem for clock languages. Journal of Automata, Languages and Combinatorics (2002) (to appear)
Bouyer, P., Petit, A., Thrien, D.: An algebraic characterization of data and timed languages. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 248–261. Springer, Heidelberg (2001)
Dima, C.: An algebraic theory of real-time formal languages. PhD thesis, Université Joseph Fourier Grenoble, France (2001)
Dima, C.: Computing reachability relations in timed automata. In: Proceedings of LICS 2002, pp. 177–186 (2002)
D’Souza, D., Thiagarajan, P.S.: Product interval automata: A subclass of timed automata. In: Pandu Rangan, C., Raman, V., Sarukkai, S. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 60–71. Springer, Heidelberg (1999)
Herrmann, P.: Timed automata and recognizability. Information Processing Letters 65, 313–318 (1998)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley/Narosa Publishing House (1992)
Larsen, K.G., Petterson, P., Yi, W.: Uppaal: Status & developments. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 456–459. Springer, Heidelberg (1997)
Yovine, S.: Model-checking timed automata. In: Rozenberg, G. (ed.) EEF School 1996. LNCS, vol. 1494, pp. 114–152. Springer, Heidelberg (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dima, C. (2004). A Nonarchimedian Discretization for Timed Languages. In: Larsen, K.G., Niebert, P. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2003. Lecture Notes in Computer Science, vol 2791. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40903-8_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-40903-8_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21671-1
Online ISBN: 978-3-540-40903-8
eBook Packages: Springer Book Archive