Skip to main content

Exploiting local persistency for reduced state-space generation

Abstract

This paper deals with two partial order techniques for Petri nets (PN in short): persistent sets and step graphs. These techniques aim to reduce the width and the depth of the marking graphs of PN, respectively, while preserving their deadlocks. To achieve more reductions while preserving the deadlocks of PN, this paper revisits the definition of persistent sets and establishes some weaker practical sufficient conditions. It also proposes a combination of persistent sets with steps as a sort of Cartesian product of persistent sets. This combination provides a means of better controlling the length and the number of steps, while still preserving deadlocks.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Notes

  1. 1.

    http://projects.laas.fr/tina//home.php.

  2. 2.

    A strong/weak-persistent selective search from a marking M is a procedure that recursively computes a weak-persistent set and the successor markings reachable by each transition of this set, for M and each new computed marking [19].

  3. 3.

    The notation \(\mu _i \models D0 \wedge D1 \wedge D2\) means that \(\mu _i\) satisfies the conditions D0, D1 and D2.

  4. 4.

    http://mcc.lip6.fr.

  5. 5.

    There is a directed path between every two nodes (places or transitions) of the Petri net.

References

  1. 1.

    Abdulla PA, Aronis S, Jonsson B, Sagonas K (2017) Source sets: a foundation for optimal dynamic partial order reduction. J ACM 64(4):25:1–25:49

    Article  MathSciNet  Google Scholar 

  2. 2.

    Barkaoui K, Boucheneb H, Li Z (2018) Exploiting local persistency for reduced state space generation. In: International conference on verification and evaluation of computer and communication systems (VECoS), volume 11181 of Lecture Notes in Computer Science, pp 166–181

  3. 3.

    Barkaoui K, Couvreur J-M, Klai K (2005) On the equivalence between liveness and deadlock-freeness in Petri nets. In: Applications and theory of Petri nets 2005, 26th international conference, ICATPN 2005, Miami, USA, June 20–25, 2005, proceedings, pp 90–107

  4. 4.

    Barkaoui K, Pradat-Peyre J-F (1996) On liveness and controlled siphons in Petri nets. In: Application and theory of Petri nets 1996, 17th international conference, Osaka, Japan, June 24–28, 1996, proceedings, pp 57–72

  5. 5.

    Chen Y (2015) Optimal supervisory control of flexible manufacturing systems. Thesis. Le Cnam

  6. 6.

    Chen YF, Li ZW, Barkaoui K (2014) New Petri net structure and its application to optimal supervisory control: interval inhibitor arcs. IEEE Trans Syst Man Cybern 44(10):1384–1400

    Article  Google Scholar 

  7. 7.

    Desel J, Juhás G (2001) ”What is a Petri net?”. In: Unifying Petri nets, advances in Petri Nets, pp 1–25

  8. 8.

    Godefroid P (1996) Partial-order methods for the verification of concurrent systems: an approach to the state-explosion problem, volume 1032 of Lecture Notes in Computer Science. Springer

  9. 9.

    Iordache MV (2006) Deadlock and liveness properties of Petri nets. Birkhäuser, Boston, pp 125–151

    Google Scholar 

  10. 10.

    Junttila T (2005) On the symmetry reduction method for Petri nets and similar formalisms. In PhD dissertation, Helsinki University of Technology, Espoo, Finland

  11. 11.

    Li ZW, Zhao M (2008) On controllability of dependent siphons for deadlock prevention in generalized Petri nets. IEEE Trans Syst Man Cybern 38(2):369–384

    Article  Google Scholar 

  12. 12.

    Peled D (1993) All from one, one for all: on model checking using representatives. In: Computer aided verification, 5th international conference, CAV ’93, Elounda, Greece, June 28–July 1, 1993, proceedings, pp 409–423

  13. 13.

    Peled D, Wilke T (1997) Stutter-invariant temporal properties are expressible without the next-time operator. Inf Process Lett 63(5):243–246

    Article  MathSciNet  Google Scholar 

  14. 14.

    Peterson JL (1981) Petri net theory and the modeling of systems. Prentice Hall PTR, Upper Saddle River

    MATH  Google Scholar 

  15. 15.

    Ribet P-O, Vernadat F, Berthomieu B (2002) On combining the persistent sets method with the covering steps graph method. In: Formal techniques for networked and distributed systems—FORTE 2002, 22nd IFIP WG 6.1 International conference Houston, Texas, USA, Nov 11–14, 2002, proceedings, pp 344–359

  16. 16.

    Valmari A (1992) A stubborn attack on state explosion. Formal Methods Syst Des 1(4):297–322

    Article  Google Scholar 

  17. 17.

    Valmari A (1996) The state explosion problem. In: Lectures on Petri nets I: basic models, advances in Petri nets, the volumes are based on the advanced course on Petri nets, held in Dagstuhl, Sept 1996, pp 429–528

  18. 18.

    Valmari A, Hansen H (2011) Can stubborn sets be optimal? Fundam Inform 113(3–4):377–397

    Article  MathSciNet  Google Scholar 

  19. 19.

    Valmari A, Hansen H (2017) Stubborn set intuition explained. Trans Petri Nets Other Models Concurr 12:140–165

    Article  MathSciNet  Google Scholar 

  20. 20.

    van der Aalst W (1998) Finding errors in the design of a workflow process: a Petri-net-based approach. In: Workflow management: net-based concepts, models, techniques, and tools (WFM ’98): proceedings of the workshop, June 22, 1998, Lisbon, Portugal, Computing Science Reports. Technische Universiteit Eindhoven, pp 60–81

  21. 21.

    Vernadat F, Azéma P, Michel F (1996) Covering step graph. In: Application and theory of Petri nets 1996, 17th international conference, Osaka, Japan, June 24–28, 1996, proceedings, pp 516–535

  22. 22.

    Wildberger NJ (2003) A new look at multiset. In: School of Mathematics, UNSW Sydney 2052, pp 1–21

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to H. Boucheneb.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Barkaoui, K., Boucheneb, H. & Li, Z. Exploiting local persistency for reduced state-space generation. Innovations Syst Softw Eng 16, 181–197 (2020). https://doi.org/10.1007/s11334-020-00358-3

Download citation

Keywords

  • Petri nets
  • Reachability analysis
  • State explosion problem
  • Persistent sets
  • Partial order techniques
  • Step graphs