Skip to main content

Checking Timed Büchi Automata Emptiness Using LU-Abstractions

  • Conference paper
Formal Modeling and Analysis of Timed Systems (FORMATS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5813))

Abstract

This paper shows that the zone-based LU-extrapolation of Behrmann et al, that preserves reachability of timed automata, also preserves emptiness of timed Büchi automata. This improves the previous results by Tripakis et al who showed that the k-extrapolation preserves timed Büchi automata emptiness. The LU-extrapolation is coarser than k-extrapolation, allowing better state space reductions. A tool with LU-extrapolation for emptiness checking of timed Büchi automata has been implemented, and some experiments are reported.

Supported by the National Natural Science Foundation of China under Grant Nos. 60673051, 60736017, 60721061.

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

Access this chapter

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alur, R.: Timed Automata. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 8–22. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  2. Aceto, L., Ingolfsdottir, A., Larsen, K., Srba, J.: Reactive Systems. In: Modelling, Specification and Verification. Cambridge University Press, Cambridge (2007)

    Chapter  Google Scholar 

  3. Aceto, L., Bouyer, P., Burgueno, A., Larsen, K.: The power of reachability testing for timed automata. Theoretical Computer Science 300(1-3), 411–475 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  5. Alur, R., Dill, D.L.: Automata-theoretic verification of real-time systems. In: Formal Methods for Real-Time Computing. Trends in Software Series, pp. 55–82. John Wiley & Sons Publishers, Chichester (1996)

    Google Scholar 

  6. Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. Journal of the ACM 43, 116–146 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Alur, R., Madhusudan, P.: Decision problems for timed automata: A survey. In: 4th Intl. School on Formal Mthods for Computer, Communication, and Software Systems: Real Time (2004)

    Google Scholar 

  8. Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press, Cambridge (2008)

    MATH  Google Scholar 

  9. Behrmann, G., Bouyer, P., Larsen, K., Pelánek, R.: Lower and upper bounds in zone-based abstractions of timed automata. STTT 8(3), 204–215 (2006)

    Article  MATH  Google Scholar 

  10. Behrmann, G., Bouyer, P., Fleury, E., Larsen, K.G.: Static Guard Analysis in Timed Automata Verification. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 254–270. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. Bengtsson, J.E., Yi, W.: Timed Automata: Semantics, Algorithms and Tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) Lectures on Concurrency and Petri Nets. LNCS, vol. 3098, pp. 87–124. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Bouyer, P.: Forward Analysis of Updatable Timed Automata. Formal Methods in System Design 24(3), 281–320 (2004)

    Article  MATH  Google Scholar 

  13. Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (1999)

    Google Scholar 

  14. Couvreur, J.-M.: On-the-fly verification of linear temporal logic. In: Wing, J.M., Woodcock, J.C.P., Davies, J. (eds.) FM 1999. LNCS, vol. 1708, pp. 253–271. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  15. Couvreur, J.-M., Duret-Lutz, A., Poitrenaud, D.: On-the-Fly Emptiness Checks for Generalized Büchi Automata. In: Godefroid, P. (ed.) SPIN 2005. LNCS, vol. 3639, pp. 169–184. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Courcoubetis, C., Vardi, M.Y., Wolper, P., Yannakakis, M.: Memory-Efficient algorithms for the verification of temporal properties. Formal Methods in System Design 1(2/3), 275–288 (1992)

    Article  MATH  Google Scholar 

  17. Kesten, Y., Manna, Z., Pnueli, A.: Verifying clocked transition systems. In: Alur, R., Sontag, E.D., Henzinger, T.A. (eds.) HS 1995. LNCS, vol. 1066, pp. 13–40. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  18. Maler, O., Nickovic, D., Pnueli, A.: From MITL to Timed Automata. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 274–289. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  19. Manna, Z., Pnueli, A.: The temporal logic of reactive and concurrent systems: Specification. Springer, New York (1992)

    Book  MATH  Google Scholar 

  20. Tripakis, S.: Checking Timed Buchi Automata Emptiness on Simulation Graphs. ACM Transactions on Computational Logic 10(3), 15:1–15:19 (2009)

    Google Scholar 

  21. Tripakis, S., Yovine, S., Bouajjani, A.: Checking Timed Büchi Automata Emptiness Efficiently. Formal Methods in System Design 26(3), 267–292 (2005)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Li, G. (2009). Checking Timed Büchi Automata Emptiness Using LU-Abstractions. In: Ouaknine, J., Vaandrager, F.W. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2009. Lecture Notes in Computer Science, vol 5813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04368-0_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04368-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04367-3

  • Online ISBN: 978-3-642-04368-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics