Skip to main content
SpringerLink
Log in

Verifying Probabilistic Timed Automata Against Omega-Regular Dense-Time Properties

  • Conference paper
  • First Online:
Quantitative Evaluation of Systems (QEST 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11024))

Included in the following conference series:

Abstract

Probabilistic timed automata (PTAs) are timed automata (TAs) extended with discrete probability distributions. They serve as a mathematical model for a wide range of applications that involve both stochastic and timed behaviours. In this work, we consider the problem of model-checking linear dense-time properties over PTAs. In particular, we study linear dense-time properties that can be encoded by TAs with infinite acceptance criterion. First, we show that the problem of model-checking PTAs against deterministic-TA specifications can be solved through a product construction. Based on the product construction, we prove that the computational complexity of the problem with deterministic-TA specifications is EXPTIME-complete. Then we show that when relaxed to general (nondeterministic) TAs, the model-checking problem becomes undecidable. Our results substantially extend state of the art with both the dense-time feature and the nondeterminism in TAs.

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

    MATH  Google Scholar 

  2. Norman, G., Parker, D., Sproston, J.: Model checking for probabilistic timed automata. Formal Methods Syst. Des. 43(2), 164–190 (2013)

    Article  Google Scholar 

  3. Beauquier, D.: On probabilistic timed automata. Theor. Comput. Sci. 292(1), 65–84 (2003)

    Article  MathSciNet  Google Scholar 

  4. Kwiatkowska, M.Z., Norman, G., Segala, R., Sproston, J.: Automatic verification of real-time systems with discrete probability distributions. Theor. Comput. Sci. 282(1), 101–150 (2002)

    Article  MathSciNet  Google Scholar 

  5. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)

    Article  MathSciNet  Google Scholar 

  6. Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York (1994)

    Book  Google Scholar 

  7. Jensen, H.E.: Model checking probabilistic real time systems. In: 7th Nordic Workshop on Programming Theory, Chalmers University of Technology, pp. 247–261 (1996)

    Google Scholar 

  8. André, É., Fribourg, L., Sproston, J.: An extension of the inverse method to probabilistic timed automata. Formal Methods Syst. Des. 42(2), 119–145 (2013)

    Article  Google Scholar 

  9. Kwiatkowska, M.Z., Norman, G., Sproston, J., Wang, F.: Symbolic model checking for probabilistic timed automata. Inf. Comput. 205(7), 1027–1077 (2007)

    Article  MathSciNet  Google Scholar 

  10. Kwiatkowska, M.Z., Norman, G., Parker, D.: Stochastic games for verification of probabilistic timed automata. In: Ouaknine, J., Vaandrager, F.W. (eds.) FORMATS 2009. LNCS, vol. 5813, pp. 212–227. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04368-0_17

    Chapter  MATH  Google Scholar 

  11. Jovanović, A., Kwiatkowska, M., Norman, G.: Symbolic minimum expected time controller synthesis for probabilistic timed automata. In: Sankaranarayanan, S., Vicario, E. (eds.) FORMATS 2015. LNCS, vol. 9268, pp. 140–155. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-22975-1_10

    Chapter  MATH  Google Scholar 

  12. Jurdziński, M., Kwiatkowska, M., Norman, G., Trivedi, A.: Concavely-priced probabilistic timed automata. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 415–430. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04081-8_28

    Chapter  Google Scholar 

  13. Kwiatkowska, M.Z., Norman, G., Parker, D., Sproston, J.: Performance analysis of probabilistic timed automata using digital clocks. Formal Methods Syst. Des. 29(1), 33–78 (2006)

    Article  Google Scholar 

  14. Berendsen, J., Chen, T., Jansen, D.N.: Undecidability of cost-bounded reachability in priced probabilistic timed automata. In: Chen, J., Cooper, S.B. (eds.) TAMC 2009. LNCS, vol. 5532, pp. 128–137. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02017-9_16

    Chapter  MATH  Google Scholar 

  15. Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_47

    Chapter  Google Scholar 

  16. Laroussinie, F., Sproston, J.: State explosion in almost-sure probabilistic reachability. Inf. Process. Lett. 102(6), 236–241 (2007)

    Article  MathSciNet  Google Scholar 

  17. Jurdzinski, M., Sproston, J., Laroussinie, F.: Model checking probabilistic timed automata with one or two clocks. LMCS 4(3), 1–28 (2008)

    MathSciNet  MATH  Google Scholar 

  18. Sproston, J.: Discrete-time verification and control for probabilistic rectangular hybrid automata. In: QEST, pp. 79–88 (2011)

    Google Scholar 

  19. Koymans, R.: Specifying real-time properties with metric temporal logic. Real Time Syst. 2(4), 255–299 (1990)

    Article  Google Scholar 

  20. Ouaknine, J., Worrell, J.: On the decidability of metric temporal logic. In: LICS, pp. 188–197 (2005)

    Google Scholar 

  21. Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. J. ACM 43(1), 116–146 (1996)

    Article  MathSciNet  Google Scholar 

  22. Donatelli, S., Haddad, S., Sproston, J.: Model checking timed and stochastic properties with CSL\(\hat{\,}\,\{TA\}\). IEEE Trans. Software Eng. 35(2), 224–240 (2009)

    Article  Google Scholar 

  23. Fu, H., Li, Y., Li, J.: Verifying probabilistic timed automata against omega-regular dense-time properties. CoRR abs/1712.00275 (2017)

    Google Scholar 

  24. Chen, T., Han, T., Katoen, J., Mereacre, A.: Model checking of continuous-time Markov chains against timed automata specifications. Log. Methods Comput. Sci. 7(1), 1–34 (2011)

    Article  MathSciNet  Google Scholar 

  25. Fu, H.: Approximating acceptance probabilities of CTMC-paths on multi-clock deterministic timed automata. In: HSCC, pp. 323–332 (2013)

    Google Scholar 

  26. Vardi, M.Y.: Probabilistic linear-time model checking: an overview of the automata-theoretic approach. In: Katoen, J.-P. (ed.) ARTS 1999. LNCS, vol. 1601, pp. 265–276. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48778-6_16

    Chapter  Google Scholar 

  27. Brázdil, T., Krcál, J., Kretínský, J., Kucera, A., Rehák, V.: Measuring performance of continuous-time stochastic processes using timed automata. In: HSCC, pp. 33–42 (2011)

    Google Scholar 

  28. Barbot, B., Chen, T., Han, T., Katoen, J.-P., Mereacre, A.: Efficient CTMC model checking of linear real-time objectives. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 128–142. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19835-9_12

    Chapter  MATH  Google Scholar 

  29. Bortolussi, L., Lanciani, R.: Fluid model checking of timed properties. In: Sankaranarayanan, S., Vicario, E. (eds.) FORMATS 2015. LNCS, vol. 9268, pp. 172–188. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-22975-1_12

    Chapter  MATH  Google Scholar 

Download references

Acknowledgements

This work has been supported by the National Natural Science Foundation of China (Grants 61761136011, 61532019, 61472473, 61772038, 61272160). We also thank anonymous reviewers for detailed comments.

Author information

Authors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Hongfei Fu

  2. Department of Informatics, School of Mathematical Sciences, Peking University, Beijing, China

    Yi Li

  3. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Jianlin Li

  4. University of Chinese Academy of Sciences, Beijing, China

    Jianlin Li

  5. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Jianlin Li

Authors
  1. Hongfei Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianlin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianlin Li .

Editor information

Editors and Affiliations

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

    Annabelle McIver

  2. University of Turin , Turin, Italy

    Andras Horvath

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Fu, H., Li, Y., Li, J. (2018). Verifying Probabilistic Timed Automata Against Omega-Regular Dense-Time Properties. In: McIver, A., Horvath, A. (eds) Quantitative Evaluation of Systems. QEST 2018. Lecture Notes in Computer Science(), vol 11024. Springer, Cham. https://doi.org/10.1007/978-3-319-99154-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-99154-2_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99153-5

  • Online ISBN: 978-3-319-99154-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation