Skip to main content
SpringerLink
Log in

Abstraction-Based Incremental Inductive Coverability for Petri Nets

  • Conference paper
  • First Online:
Application and Theory of Petri Nets and Concurrency (PETRI NETS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12734))

Abstract

We present a novel approach to check the coverability problem of Petri nets which is based on a tight integration of IC3 with place-merge abstraction. Place-merge abstraction can reduce the dimensionality of state spaces by trying to merge some places that may be not critical for proving the property. In this scenario, IC3 runs only on abstract Petri nets with lower dimensionality. When the current abstraction allows for a spurious counterexample, it is refined by splitting candidate abstract places. Furthermore, this can be done in a completely incremental way without discarding results found in previous abstractions. The experimental evaluation on the standard Petri net benchmarks shows the effectiveness and competitiveness of our approach.

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

Notes

  1. 1.

    https://github.com/pierreganty/mist.

References

  1. Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.: General decidability theorems for infinite-state systems. In: Proceedings, 11th Annual IEEE Symposium on Logic in Computer Science, 1996. pp. 313–321. IEEE Computer Society (1996). https://doi.org/10.1109/LICS.1996.561359

  2. Batz, K., Junges, S., Kaminski, B.L., Katoen, J.-P., Matheja, C., Schröer, P.: PrIC3: property directed reachability for MDPs. In: Lahiri, S.K., Wang, C. (eds.) CAV 2020. LNCS, vol. 12225, pp. 512–538. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-53291-8_27

    Chapter  Google Scholar 

  3. Birgmeier, J., Bradley, A.R., Weissenbacher, G.: Counterexample to Induction-Guided Abstraction-Refinement (CTIGAR). In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 831–848. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_55

    Chapter  Google Scholar 

  4. Bradley, A.R.: SAT-based model checking without unrolling. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-18275-4_7

    Chapter  Google Scholar 

  5. Cimatti, A., Griggio, A.: Software model checking via IC3. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 277–293. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31424-7_23

    Chapter  Google Scholar 

  6. Cimatti, A., Griggio, A., Mover, S., Tonetta, S.: IC3 modulo theories via implicit predicate abstraction. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 46–61. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54862-8_4

    Chapter  MATH  Google Scholar 

  7. Cimatti, A., Griggio, A., Mover, S., Tonetta, S.: Infinite-state invariant checking with IC3 and predicate abstraction. Formal Methods Syst. Des. 49(3), 190–218 (2016). https://doi.org/10.1007/s10703-016-0257-4

    Article  MATH  Google Scholar 

  8. Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. J. ACM (JACM) 50(5), 752–794 (2003). https://doi.org/10.1145/876638.876643

    Article  MathSciNet  MATH  Google Scholar 

  9. Clarke, E.M., Grumberg, O., Long, D.E.: Model checking and abstraction. ACM Trans. Programm. Lang. Syst. (TOPLAS) 16(5), 1512–1542 (1994). https://doi.org/10.1145/186025.186051

    Article  Google Scholar 

  10. Eén, N., Mishchenko, A., Brayton, R.K.: Efficient implementation of property directed reachability. In: Bjesse, P., Slobodová, A. (eds.) International Conference on Formal Methods in Computer-Aided Design, FMCAD 2011, pp. 125–134. FMCAD Inc. (2011)

    Google Scholar 

  11. Esparza, J., Ledesma-Garza, R., Majumdar, R., Meyer, P., Niksic, F.: An SMT-based approach to coverability analysis. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 603–619. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_40

    Chapter  Google Scholar 

  12. Finkel, A., Leroux, J.: Recent and simple algorithms for Petri nets. Softw. Syst. Model. 14(2), 719–725 (2014). https://doi.org/10.1007/s10270-014-0426-0

    Article  Google Scholar 

  13. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theor. Comput. Sci. 256(1–2), 63–92 (2001)

    Article  MathSciNet  Google Scholar 

  14. Ganty, P., Raskin, J.-F., Van Begin, L.: From many places to few: automatic abstraction refinement for petri nets. In: Kleijn, J., Yakovlev, A. (eds.) ICATPN 2007. LNCS, vol. 4546, pp. 124–143. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73094-1_10

    Chapter  MATH  Google Scholar 

  15. Jones, N.D., Landweber, L.H., Lien, Y.E.: Complexity of some problems in Petri nets. Theor. Comput. Sci. 4(3), 277–299 (1977)

    Article  MathSciNet  Google Scholar 

  16. Kaiser, A., Kroening, D., Wahl, T.: Efficient coverability analysis by proof minimization. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 500–515. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32940-1_35

    Chapter  Google Scholar 

  17. Kindermann, R., Junttila, T., Niemelä, I.: SMT-based induction methods for timed systems. In: Jurdziński, M., Ničković, D. (eds.) FORMATS 2012. LNCS, vol. 7595, pp. 171–187. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33365-1_13

    Chapter  MATH  Google Scholar 

  18. Kloos, J., Majumdar, R., Niksic, F., Piskac, R.: Incremental, inductive coverability. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 158–173. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_10

    Chapter  Google Scholar 

  19. Lange, T., Neuhäußer, M.R., Noll, T., Katoen, J.-P.: IC3 software model checking. Int. J. Softw. Tools Technol. Transf. 22(2), 135–161 (2019). https://doi.org/10.1007/s10009-019-00547-x

    Article  Google Scholar 

  20. Majumdar, R., Meyer, R., Wang, Z.: Static provenance verification for message passing programs. In: Logozzo, F., Fähndrich, M. (eds.) SAS 2013. LNCS, vol. 7935, pp. 366–387. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38856-9_20

    Chapter  Google Scholar 

  21. Reisig, W.: Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer Science, vol. 4. Springer (1985)

    Google Scholar 

Download references

Acknowledgements

We thank Dr. Weifeng Wang for helpful suggestions on this paper, and we also thank the anonymous referees for their constructive comments. This work is partly funded by NSFC-62072443 and NSFC-61972385.

Author information

Authors and Affiliations

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

    Jiawen Kang, Yunjun Bai & Li Jiao

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

    Jiawen Kang, Yunjun Bai & Li Jiao

Authors
  1. Jiawen Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yunjun Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Li Jiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li Jiao .

Editor information

Editors and Affiliations

  1. Université de Genève, Carouge, Switzerland

    Didier Buchs

  2. Universitat Politècnica de Catalunya, Barcelona, Spain

    Josep Carmona

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kang, J., Bai, Y., Jiao, L. (2021). Abstraction-Based Incremental Inductive Coverability for Petri Nets. In: Buchs, D., Carmona, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2021. Lecture Notes in Computer Science(), vol 12734. Springer, Cham. https://doi.org/10.1007/978-3-030-76983-3_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-76983-3_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-76982-6

  • Online ISBN: 978-3-030-76983-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation