Abstract
We show that stopwatch automata are equivalent to timed shuffle expressions, an extension of timed regular expressions with the shuffle operation. This implies that the emptiness problem for timed shuffle expressions is undecidable. The result holds for both timed state sequence semantics and timed event sequence semantics of automata and expressions.
Similarly to timed regular expressions, our timed shuffle expressions employ renaming. But we show that even when renaming is not used, shuffle regular expressions still have an undecidable emptiness problem. This solves in the negative a conjecture of Asarin on the possibility to use shuffle to define timed regular languages.
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.
Partially supported by the PAI “Brancusi” no. 08797XL.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)
Asarin, E.: Challenges in timed languages. Bulletin of EATCS 83 (2004)
Asarin, E., Caspi, P., Maler, O.: A Kleene theorem for timed automata. In: Proceedings of LICS 1997, pp. 160–171 (1997)
Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. Journal of ACM 49, 172–206 (2002)
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, p. 210. Springer, Heidelberg (1999)
Dima, C.: Kleene theorems for event-clock automata. In: Ciobanu, G., Păun, G. (eds.) FCT 1999. LNCS, vol. 1684, pp. 215–225. Springer, Heidelberg (1999)
Dima, C.: Real-time automata. Journal of Automata, Languages and Combinatorics 6, 3–23 (2001)
Dima, C.: A nonarchimedian discretization for timed languages. In: Larsen, K.G., Niebert, P. (eds.) FORMATS 2003. LNCS, vol. 2791, pp. 161–181. Springer, Heidelberg (2004)
Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata. J. Comput. Syst. Sci 57, 94–124 (1998)
Herrmann, P.: Renaming is necessary in timed regular expressions. In: Pandu Rangan, C., Raman, V., Sarukkai, S. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 47–59. Springer, Heidelberg (1999)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley/Narosa Publishing House (1992)
Krcál, P., Yi, W.: Decidable and undecidable problems in schedulability analysis using timed automata. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 236–250. Springer, Heidelberg (2004)
Ouaknine, J., Worrell, J.: Revisiting digitization, robustness, and decidability for timed automata. In: Proceedings of LICS 2003, pp. 198–207. IEEE Computer Society Press, Los Alamitos (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dima, C. (2005). Timed Shuffle Expressions. In: Abadi, M., de Alfaro, L. (eds) CONCUR 2005 – Concurrency Theory. CONCUR 2005. Lecture Notes in Computer Science, vol 3653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11539452_11
Download citation
DOI: https://doi.org/10.1007/11539452_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28309-6
Online ISBN: 978-3-540-31934-4
eBook Packages: Computer ScienceComputer Science (R0)