Skip to main content

Interval Abstraction Refinement for Model Checking of Timed-Arc Petri Nets

  • Conference paper
Formal Modeling and Analysis of Timed Systems (FORMATS 2014)

Abstract

State-space explosion is a major obstacle in verification of time-critical distributed systems. An important factor with a negative influence on the tractability of the analysis is the size of constants that clocks are compared to. This problem is particularly accented in explicit state-space exploration techniques. We suggest an approximation method for reducing the size of constants present in the model. The proposed method is developed for Timed-Arc Petri Nets and creates an under-approximation or an over-approximation of the model behaviour. The verification of approximated Petri net models can be considerably faster but it does not in general guarantee conclusive answers. We implement the algorithms within the open-source model checker TAPAAL and demonstrate on a number of experiments that our approximation techniques often result in a significant speed-up of the verification.

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Alur, R., Itai, A., Kurshan, R., Yannakakis, M.: Timing verification by successive approximation. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 137–150. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  3. Andersen, M., Gatten Larsen, H., Srba, J., Grund Sørensen, M., Haahr Taankvist, J.: Verification of liveness properties on closed timed-arc Petri nets. In: Kučera, A., Henzinger, T.A., Nešetřil, J., Vojnar, T., Antoš, D. (eds.) MEMICS 2012. LNCS, vol. 7721, pp. 69–81. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Asarin, E., Maler, O., Pnueli, A.: On discretization of delays in timed automata and digital circuits. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 470–484. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  5. Bolognesi, T., Lucidi, F., Trigila, S.: From timed Petri nets to timed LOTOS. In: IFIP WG 6.1 Tenth International Symposium on Protocol Specification, Testing and Verification, pp. 1–14. North-Holland, Amsterdam (1990)

    Google Scholar 

  6. Bozga, M., Maler, O., Tripakis, S.: Efficient verification of timed automata using dense and discrete time semantics. In: Pierre, L., Kropf, T. (eds.) CHARME 1999. LNCS, vol. 1703, pp. 125–141. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  7. Cicirelli, F., Furfaro, A., Nigro, L.: Model checking time-dependent system specifications using time stream Petri nets and UPPAAL. Applied Mathematics and Computation 218(16), 8160–8186 (2012)

    Article  MATH  Google Scholar 

  8. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  9. Clarke, E.M., Grumberg, O., Long, D.E.: Model checking and abstraction. ACM Trans. Program. Lang. Syst. 16(5), 1512–1542 (1994)

    Article  Google Scholar 

  10. David, A., Jacobsen, L., Jacobsen, M., Jørgensen, K.Y., Møller, M.H., Srba, J.: TAPAAL 2.0: Integrated development environment for timed-arc Petri nets. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 492–497. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. David, A., Jacobsen, L., Jacobsen, M., Srba, J.: A forward reachability algorithm for bounded timed-arc Petri nets. In: SSV 2012. EPTCS, vol. 102, pp. 125–140. Open Publishing Association (2012)

    Google Scholar 

  12. Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  13. Dill, D.L., Wong-Toi, H.: Verification of real-time systems by successive over and under approximation. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 409–422. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  14. Drægert, A., Kaysen, A.C., Byrdal Kjær, J., Mikkelsen, F.B., Nduru, C., Petersen, D.S.: LEGO car safety systems. 5th Semester Software Engineer Project Report, Aalborg University (2014)

    Google Scholar 

  15. Hanisch, H.M.: Analysis of place/transition nets with timed-arcs and its application to batch process control. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, pp. 282–299. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  16. Jensen, P.G., Larsen, K.G., Srba, J., Sørensen, M.G., Taankvist, J.H.: Memory efficient data structures for explicit verification of timed systems. In: Badger, J.M., Rozier, K.Y. (eds.) NFM 2014. LNCS, vol. 8430, pp. 307–312. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  17. Jørgensen, K.Y., Larsen, K.G., Srba, J.: Time-darts: A data structure for verification of closed timed automata. In: SSV 2012. EPTCS, vol. 102, pp. 141–155. Open Publishing Association (2012)

    Google Scholar 

  18. Marques Jr., A.P., Ravn, A.P., Srba, J., Vighio, S.: Model-checking web services business activity protocols. International Journal on Software Tools for Technology Transfer (STTT) 15(2), 125–147 (2013)

    Article  Google Scholar 

  19. Lamport, L.: Real-time model checking is really simple. In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 162–175. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Larsen, K.G., Behrmann, G., Skou, A.: Exercises for UPPAAL (2008), http://www.cs.aau.dk/~bnielsen/TOV08/ESV04/exercises

  21. Lee, W., Pardo, A., Jang, J.-Y., Hachtel, G., Somenzi, F.: Tearing based automatic abstraction for CTL model checking. In: ICCAD 1996, pp. 76–81. IEEE Computer Society (1996)

    Google Scholar 

  22. Merlin, P.M., Faber, D.J.: Recoverability of communication protocols: Implications of a theoretical study. IEEE Trans. on Comm. 24(9), 1036–1043 (1976)

    Article  MATH  Google Scholar 

  23. Murata, T.: State equation, controllability, and maximal matchings of Petri nets. IEEE Trans. on Automatic Control 22(3), 412–416 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  24. Pardo, A., Hachtel, G.D.: Incremental CTL model checking using BDD subsetting. In: DAC 1998, pp. 457–462. ACM (1998)

    Google Scholar 

  25. Popova-Zeugmann, L.: On time Petri nets. Elektronische Informationsverarbeitung und Kybernetik 27(4), 227–244 (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Viesmose Birch, S., Stig Jacobsen, T., Jon Jensen, J., Moesgaard, C., Nørgaard Samuelsen, N., Srba, J. (2014). Interval Abstraction Refinement for Model Checking of Timed-Arc Petri Nets. In: Legay, A., Bozga, M. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2014. Lecture Notes in Computer Science, vol 8711. Springer, Cham. https://doi.org/10.1007/978-3-319-10512-3_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10512-3_17

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10511-6

  • Online ISBN: 978-3-319-10512-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics