Skip to main content
SpringerLink
Log in

Relevant Timed Schedules/Clock Vectors for Constructing Time Petri Net Reachability Graphs

  • Published:
Discrete Event Dynamic Systems Aims and scope Submit manuscript

Abstract

We consider here the time Petri nets (the TPN model) and its state space abstractions. We show that only some timed schedules/clock vectors (one per enabled transition) of the clock/firing domains are relevant to construct reachability graphs for the TPN. Moreover, we prove formally that the resulting graphs are smaller than the TPN reachability graphs proposed in the literature. Furthermore, these results establish a relation between dense time and discrete time analysis of time Petri nets and allow also improving discrete time analysis by considering only some elements of the clock/firing domains.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

Notes

  1. An integer clock state is a state whose clock values are integer numbers.

  2. An atomic constraint is of the form x − y ≤ c, x ≤ c or − x ≤ c, where x, y are real valued variables representing clocks or intervals (remaining times), c ∈ ℚ ∪ { ∞ } and ℚ is the set of rational numbers (for economy of notation, we use operator ≤ even if c = ∞).

References

  • Behrmann G, Bouyer P, Larsen KG, Pelànek R (2006) Lower and upper bounds in zone-based abstractions of timed automata. Int J Softw Tools Technol Transf 8(3):204–215

    Article  Google Scholar 

  • Bengtsson J (2002) Clocks, DBMs and states in timed systems. PhD thesis, Dept. of Information Technology, Uppsala University

  • Berthomieu B, Peres F, Vernadat F (2007) Model-checking bounded prioriterized time Petri nets. In: Proceedings of ATVA 2007. LNCS, vol 4762

  • Berthomieu B, Vernadat F (2003) State class constructions for branching analysis of time Petri nets. LNCS 2619:442–457

    Google Scholar 

  • Boucheneb H, Gardey G, Roux OH (2009) TCTL model checking of time Petri nets. J Log Comput 19(6):1509–1540. doi:10.1093/logcom/exp036

    Article  MATH  MathSciNet  Google Scholar 

  • Boucheneb H, Rakkay H (2007) A more efficient time Petri net state space abstraction preserving linear properties. In: Proc. of the seventh international conference on application of concurrency to system design (ACSD 2007). IEEE Computer Society, pp 61–70

  • Boucheneb H, Hadjidj R (2006) CTL* model checking for time Petri nets. Journal of Theoretical Computer Science TCS 353/1–3:208–227

    Google Scholar 

  • Cormen TH, Leiserson CE, Rivest RL, Stein C (2002) Introduction to algorithms, 2nd edn. The MIT Press

  • Gardey G, Roux OH, Roux OF (2006) State space computation and analysis of time Petri nets. Theory and Practice of Logic Programming (TPLP) 6(3):301–320

    Article  MATH  MathSciNet  Google Scholar 

  • Hadjidj R, Boucheneb H (2009) On-the-fly TCTL model checking for time Petri nets. Journal of Theoretical Computer Science TCS 410(42):4241–4261

    Article  MATH  MathSciNet  Google Scholar 

  • Penczek W, Pólrola A (2004) Specification and model checking of temporal properties in time Petri nets and timed automata. In: Proc. of ICATPN, LNCS, vol 3099. Springer–Verlag, pp 37–76

  • Popova-Zeugmann L, Schlatter D (1999) Analyzing paths in time Petri nets. Fundam Inform 37:311–327

    MATH  MathSciNet  Google Scholar 

  • Popova-Zeugmann L (1998) Essential states in time Petri nets. Informatik-Berichte 96:1–14

    Google Scholar 

  • Yoneda T, Schlingloff BH (1997) Efficient verification of parallel real-time systems. Form Methods Syst Des 11(2):187–215

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank the anonymous reviewers for their detailed comments that really contributed to improve the presentation of this paper.

Author information

Authors and Affiliations

  1. Laboratoire VeriForm, Department of Computer Engineering, École Polytechnique de Montréal, P.O. Box 6079, Station Centre-ville, Montréal, Québec, Canada, H3C 3A7

    Hanifa Boucheneb

  2. Laboratoire CEDRIC, Conservatoire National des Arts et Métiers, 292 rue Saint Martin, Paris, Cedex 03, France

    Kamel Barkaoui

Authors
  1. Hanifa Boucheneb
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kamel Barkaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hanifa Boucheneb.

Additional information

A reachability graph of a TPN is an abstraction of its state space preserving markings and traces (its linear properties).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boucheneb, H., Barkaoui, K. Relevant Timed Schedules/Clock Vectors for Constructing Time Petri Net Reachability Graphs. Discrete Event Dyn Syst 21, 171–204 (2011). https://doi.org/10.1007/s10626-011-0100-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10626-011-0100-4

Keywords

Search

Navigation