Skip to main content
SpringerLink
Log in

Synchronized Recursive Timed Automata

  • Conference paper
  • First Online:
Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9450))

Included in the following conference series:

  • 808 Accesses

Abstract

We present synchronized recursive timed automata (SRTA) that extend timed automata with a stack. Each frame of a stack is composed of rational-valued clocks, and SRTA synchronously increase the values of all the clocks within the stack. Our main contribution is to show that the reachability problem of SRTA is ExpTime-complete. This decidability contrasts with the undecidability for recursive timed automata (RTA) introduced by Trivedi and Wojtczak, and Benerecetti et al. Unlike SRTA, the frames below the top are frozen during the computation at the top frame in RTA.

Our construction of the decidability proof is based on the region abstraction for dense timed pushdown automata (TPDA) of Abdulla et al. to accommodate together diagonal constraints and fractional constraints of SRTA. Since SRTA can be seen as an extension of TPDA with diagonal and fractional constraints, our result enlarges the decidable class of pushdown-extensions of timed automata.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abdulla, P., Atig, M., Stenman, J.: Dense-timed pushdown automata. In: LICS 2012, pp. 35–44. IEEE (2012)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Benerecetti, M., Minopoli, S., Peron, A.: Analysis of timed recursive state machines. In: TIME, pp. 61–68. IEEE (2010)

    Google Scholar 

  4. Bérard, B., Diekert, V., Gastin, P., Petit, A.: Characterization of the expressive power of silent transitions in timed automata. Fundam. Inf. 36(2), 145–182 (1998)

    MATH  Google Scholar 

  5. Bouajjani, A., Esparza, J., Maler, O.: Reachability analysis of pushdown automata: Application to model-checking. In: Mazurkiewicz, A., Winkowski, j (eds.) CONCUR ’97: Concurrency Theory. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  6. Bouyer, P., Dufourd, C., Fleury, E., Petit, A.: Updatable timed automata. TCS 321(2–3), 291–345 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Büchi, J.: Regular canonical systems. Arch. Math. Logik Grundlag 6, 91–111 (1964)

    Article  MATH  Google Scholar 

  8. Clemente, L., Lasota, S.: Timed pushdown automata revisited. In: LICS 2015, pp. 738–749. IEEE (2015)

    Google Scholar 

  9. Finkel, A., Willems, B., Wolper, P.: A direct symbolic approach to model checking pushdown systems. In: INFINITY 1997, pp. 27–37. Elsevier (1997)

    Google Scholar 

  10. Krishna, S., Manasa, L., Trivedi, A.: What’s decidable about recursive hybrid automata? In: HSCC 2015, pp. 31–40. ACM (2015)

    Google Scholar 

  11. Lynch, N., Vaandrager, F.: Forward and backward simulations. Inf. Comp. 121(2), 214–233 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  12. Trivedi, A., Wojtczak, D.: Recursive timed automata. In: Bouajjani, A., Chin, W.-N. (eds.) ATVA 2010. LNCS, vol. 6252, pp. 306–324. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  13. Uezato, Y., Minamide, Y.: Synchronized recursive timed automata (2015). http://score.cs.tsukuba.ac.jp/~uezato/SRTA.pdf

Download references

Acknowledgement

This work was supported by JSPS KAKENHI Grant Number 15J01843 and 15K00087.

Author information

Authors and Affiliations

  1. University of Tsukuba, Tsukuba, Japan

    Yuya Uezato

  2. Tokyo Institute of Technology, Tokyo, Japan

    Yasuhiko Minamide

Authors
  1. Yuya Uezato
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yasuhiko Minamide
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuya Uezato .

Editor information

Editors and Affiliations

  1. New York University, New York, New York, USA

    Martin Davis

  2. University of the South Pacific, Suva, Fiji

    Ansgar Fehnker

  3. Macquarie University, Sydney, New South Wales, Australia

    Annabelle McIver

  4. The University of Manchester, Manchester, United Kingdom

    Andrei Voronkov

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Uezato, Y., Minamide, Y. (2015). Synchronized Recursive Timed Automata. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2015. Lecture Notes in Computer Science(), vol 9450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48899-7_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-48899-7_18

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48898-0

  • Online ISBN: 978-3-662-48899-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation