Abstract
In this paper, we propose an abstract procedure which, given a timed automaton, produces a language-equivalent deterministic infinite timed tree. We prove that under a certain boundedness condition, the infinite timed tree can be reduced into a classical deterministic timed automaton. The boundedness condition is satisfied by several subclasses of timed automata, some of them were known to be determinizable (event-clock timed automata, automata with integer resets), but some others were not. We prove for instance that strongly non-Zeno timed automata can be determinized. As a corollary of those constructions, we get for those classes the decidability of the universality and of the inclusion problems, and compute their complexities (the inclusion problem is for instance EXPSPACE-complete for strongly non-Zeno timed automata).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Adams, S., Ouaknine, J., Worrell, J.: Undecidability of universality for timed automata with minimal resources. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 25–37. Springer, Heidelberg (2007)
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Alur, R., Fix, L., Henzinger, T.A.: A determinizable class of timed automata. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 1–13. Springer, Heidelberg (1994)
Asarin, E., Maler, O., Pnueli, A., Sifakis, J.: Controller synthesis for timed automata. In: Proc. IFAC Symposium on System Structure and Control, pp. 469–474. Elsevier Science, Amsterdam (1998)
Baier, C., Bertrand, N., Bouyer, P., Brihaye, T.: When are timed automata determinizable? Research Report LSV-09-08, Laboratoire Spécification & Vérification, ENS de Cachan, France (2009)
Finkel, O.: Undecidable problems about timed automata. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 187–199. Springer, Heidelberg (2006)
Ouaknine, J., Worrell, J.: On the language inclusion problem for timed automata: Closing a decidability gap. In: Proc. 19th Annual Symposium on Logic in Computer Science (LICS 2004), pp. 54–63. IEEE Computer Society Press, Los Alamitos (2004)
Ouaknine, J., Worrell, J.: On the decidability and complexity of metric temporal logic over finite words. Logical Methods in Computer Science 3(1:8) (2007)
Suman, P.V., Pandya, P.K., Krishna, S.N., Manasa, L.: Timed automata with integer resets: Language inclusion and expressiveness. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 78–92. Springer, Heidelberg (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baier, C., Bertrand, N., Bouyer, P., Brihaye, T. (2009). When Are Timed Automata Determinizable?. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02930-1_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-02930-1_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02929-5
Online ISBN: 978-3-642-02930-1
eBook Packages: Computer ScienceComputer Science (R0)