Skip to main content

The Inconsistent Labelling Problem of Stutter-Preserving Partial-Order Reduction

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12077)

Abstract

In model checking, partial-order reduction (POR) is an effective technique to reduce the size of the state space. Stubborn sets are an established variant of POR and have seen many applications over the past 31 years. One of the early works on stubborn sets shows that a combination of several conditions on the reduction is sufficient to preserve stutter-trace equivalence, making stubborn sets suitable for model checking of linear-time properties. In this paper, we identify a flaw in the reasoning and show with a counter-example that stutter-trace equivalence is not necessarily preserved. We propose a solution together with an updated correctness proof. Furthermore, we analyse in which formalisms this problem may occur. The impact on practical implementations is limited, since they all compute a correct approximation of the theory.

References

  1. Baier, C., Katoen, J.P.: Principles of model checking. MIT Press (2008)

    Google Scholar 

  2. Beneš, N., Brim, L., Buhnova, B., Ern, I., Sochor, J., Vařeková, P.: Partial order reduction for state/event LTL with application to component-interaction automata. Science of Computer Programming 76(10), 877–890 (2011). https://doi.org/10.1016/j.scico.2010.02.008

  3. Beneš, N., Brim, L., Černá, I., Sochor, J., Vařeková, P., Zimmerova, B.: Partial Order Reduction for State/Event LTL. In: IFM 2009. LNCS, vol. 5423, pp. 307–321 (2009). https://doi.org/10.1007/978-3-642-00255-7_21

  4. Bønneland, F.M., Jensen, P.G., Larsen, K.G., Muñiz, M.: Partial Order Reduction for Reachability Games. In: CONCUR 2019. vol. 140, pp. 23:1–23:15 (2019). https://doi.org/10.4230/LIPIcs.CONCUR.2019.23

  5. Gerth, R., Kuiper, R., Peled, D., Penczek, W.: A Partial Order Approach to Branching Time Logic Model Checking. Information and Computation 150(2), 132–152 (1999). https://doi.org/10.1006/inco.1998.2778

  6. Gibson-Robinson, T., Hansen, H., Roscoe, A.W., Wang, X.: Practical Partial Order Reduction for CSP. In: NFM 2015. LNCS, vol. 9058, pp. 188–203 (2015). https://doi.org/10.1007/978-3-319-17524-9_14

  7. Godefroid, P.: Partial-Order Methods for the Verification of Concurrent Systems, LNCS, vol. 1032. Springer (1996). https://doi.org/10.1007/3-540-60761-7

  8. Hansen, H., Lin, S., Liu, Y., Nguyen, T.K., Sun, J.: Diamonds Are a Girl’s Best Friend: Partial Order Reduction for Timed Automata with Abstractions. In: CAV 2014. LNCS, vol. 8559, pp. 391–406 (2014). https://doi.org/10.1007/978-3-319-08867-9_26

  9. Laarman, A., Pater, E., van de Pol, J., Hansen, H.: Guard-based partial-order reduction. STTT 18(4), 427–448 (2016). https://doi.org/10.1007/s10009-014-0363-9

  10. Liebke, T., Wolf, K.: Taking Some Burden Off an Explicit CTL Model Checker. In: Petri Nets 2019. LNCS, vol. 11522, pp. 321–341 (2019). https://doi.org/10.1007/978-3-030-21571-2_18

  11. Peled, D.: All from One, One for All: on Model Checking Using Representatives. In: CAV 1993. LNCS, vol. 697, pp. 409–423 (1993). https://doi.org/10.1007/3-540-56922-7_34

  12. Peled, D.: Combining partial order reductions with on-the-fly model-checking. FMSD 8(1), 39–64 (1996). https://doi.org/10.1007/BF00121262

  13. Schmidt, K.: Stubborn sets for model checking the EF/AG fragment of CTL. Fundamenta Informaticae 43(1-4), 331–341 (2000)

    Google Scholar 

  14. Siegel, S.F.: What’s Wrong with On-the-Fly Partial Order Reduction. In: CAV 2019. LNCS, vol. 11562, pp. 478–495 (2019). https://doi.org/10.1007/978-3-030-25543-5_27

  15. Valmari, A.: A Stubborn Attack on State Explosion. In: CAV 1990. LNCS, vol. 531, pp. 156–165 (1991). https://doi.org/10.1007/BFb0023729

  16. Valmari, A.: Stubborn sets for reduced state space generation. In: Advances in Petri Nets. vol. 483, pp. 491–515 (1991). https://doi.org/10.1007/3-540-53863-1_36

  17. Valmari, A.: A Stubborn Attack on State Explosion. Formal Methods in System Design 1(4), 297–322 (1992). https://doi.org/10.1007/BF00709154

  18. Valmari, A.: The state explosion problem. In: ACPN 1996. LNCS, vol. 1491, pp. 429–528 (1996). https://doi.org/10.1007/3-540-65306-6_21

  19. Valmari, A.: Stubborn Set Methods for Process Algebras. In: POMIV 1996. DIMACS, vol. 29, pp. 213–231 (1997). https://doi.org/10.1090/dimacs/029/12

  20. Valmari, A.: Stop It, and Be Stubborn! TECS 16(2), 46:1–46:26 (2017). https://doi.org/10.1145/3012279

  21. Valmari, A., Hansen, H.: Stubborn Set Intuition Explained. In: ToPNoC XII. LNCS, vol. 10470, pp. 140–165 (2017). https://doi.org/10.1007/978-3-662-55862-1_7

  22. Varpaaniemi, K.: On Stubborn Sets in the Verification of Linear Time Temporal Properties. FMSD 26(1), 45–67 (2005). https://doi.org/10.1007/s10703-005-4594-y

  23. Wolf, K.: Petri Net Model Checking with LoLA 2. In: Petri Nets 2018. LNCS, vol. 10877, pp. 351–362 (2018). https://doi.org/10.1007/978-3-319-91268-4_18

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thomas Neele .

Editor information

Editors and Affiliations

Rights and permissions

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Reprints and Permissions

Copyright information

© 2020 The Author(s)

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Neele, T., Valmari, A., Willemse, T.A.C. (2020). The Inconsistent Labelling Problem of Stutter-Preserving Partial-Order Reduction. In: Goubault-Larrecq, J., König, B. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2020. Lecture Notes in Computer Science(), vol 12077. Springer, Cham. https://doi.org/10.1007/978-3-030-45231-5_25

Download citation