Complexity of the Soundness Problem of Bounded Workflow Nets

  • Guan Jun Liu
  • Jun Sun
  • Yang Liu
  • Jin Song Dong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7347)

Abstract

Classical workflow nets (WF-nets) are an important class of Petri nets that are widely used to model and analyze workflow systems. Soundness is a crucial property that guarantees these systems are deadlock-free and bounded. Aalst et al. proved that the soundness problem is decidable, and proposed (but not proved) that the soundness problem is EXPSPACE-hard. In this paper, we show that the satisfiability problem of Boolean expression is polynomial time reducible to the liveness problem of bounded WF-nets, and soundness and liveness are equivalent for bounded WF-nets. As a result, the soundness problem of bounded WF-nets is co-NP-hard.

Workflow nets with reset arcs (reWF-nets) are an extension to WF-nets, which enhance the expressiveness of WF-nets. Aalst et al. proved that the soundness problem of reWF-nets is undecidable. In this paper, we show that for bounded reWF-nets, the soundness problem is decidable and equivalent to the liveness problem. Furthermore, a bounded reWF-net can be constructed in polynomial time for every linear bounded automaton (LBA) with an input string, and we prove that the LBA accepts the input string if and only if the constructed reWF-net is live. As a result, the soundness problem of bounded reWF-nets is PSPACE-hard.

Keywords

Petri nets workflow nets workflow nets with reset arcs soundness co-NP-hardness PSPACE-hardness 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Van der Aalst, W.M.P.: Interorganizational Workflows: An Approach Based on Message Sequence Charts and Petri Nets. System Analysis and Modeling 34, 335–367 (1999)MATHGoogle Scholar
  2. 2.
    Van der Aalst, W.M.P.: Loosely Coupled Interorganizational Wokflows: Modeling and Analyzing Workflows Crossing Organizational Boundaries. Inf. Manage. 37, 67–75 (2000)CrossRefGoogle Scholar
  3. 3.
    Van der Aalst, W.M.P.: Structural Characterizations of Sound Workflow Nets. Computing Science Report 96/23, Eindhoven University of Technology (1996)Google Scholar
  4. 4.
    Van der Aalst, W.M.P., Van Hee, K.M., Ter Hofstede, A.H.M., Sidorova, N., Verbeek, H.M.W., Voorhoeve, M., Wynn, M.T.: Soundness of Workflow Nets: Classification, Decidability, and Analysis. Formal Aspects of Computing 23, 333–363 (2011)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Cheng, A., Esparza, J., Palsberg, J.: Complexity Results for 1-safe Nets. Theoretical Computer Science 147, 117–136 (1995)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Desel, J., Esparza, J.: Free Choice Petri Nets. Cambridge Tracts in Theoretical Computer Science, vol. 40. Cambridge University Press, Cambridge (1995)MATHCrossRefGoogle Scholar
  7. 7.
    Dufourd, C., Finkel, A., Schnoebelen, P.: Reset Nets Between Decidability and Undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 103–115. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  8. 8.
    Dufourd, C., Jančar, P., Schnoebelen, P.: Boundedness of Reset P/T Nets. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 301–310. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  9. 9.
    Garey, M.R., Johnson, D.S.: Computer and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company (1976)Google Scholar
  10. 10.
    Hack, M.: Petri Net Languages. Technical Report 159. MIT (1976)Google Scholar
  11. 11.
    van Hee, K.M., Sidorova, N., Voorhoeve, M.: Generalised Soundness of Workflow Nets Is Decidable. In: Cortadella, J., Reisig, W. (eds.) ICATPN 2004. LNCS, vol. 3099, pp. 197–215. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Kang, M.H., Park, J.S., Froscher, J.N.: Access Control Mechanisms for Inter-organizational Workflow. In: Proc. of the Sixth ACM Symposium on Access Control Models and Technologies, pp. 66–74. ACM Press, New York (2001)CrossRefGoogle Scholar
  13. 13.
    Kindler, E.: The ePNK: An Extensible Petri Net Tool for PNML. In: Kristensen, L.M., Petrucci, L. (eds.) PETRI NETS 2011. LNCS, vol. 6709, pp. 318–327. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Kindler, E., Martens, A., Reisig, W.: Inter-operability of Workflow Applications: Local Criteria for Global Soundness. In: van der Aalst, W.M.P., Desel, J., Oberweis, A. (eds.) BPM 2000. LNCS, vol. 1806, pp. 235–253. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  15. 15.
    Ohta, A., Tsuji, K.: NP-hardness of Liveness Problem of Bounded Asymmetric Choice Net. IEICE Trans. Fundamentals E85-A, 1071–1074 (2002)Google Scholar
  16. 16.
    Tiplea, F.L., Bocaneala, C.: Decidability Results for Soundness Criteria of Resource-Constrained Workflow Nets. IEEE Trans. on Systems, man, and Cybernetics, Part A: Systems and Humans 42, 238–249 (2011)CrossRefGoogle Scholar
  17. 17.
    Verbeek, H.M.W., Van der Aalst, W.M.P., Ter Hofstede, A.H.M.: Verifying Worklows with Cancellation Regions and OR-joins: An Approach Based on Relaxed Soundness and Invariants. Computer Journal 50, 294–314 (2007)CrossRefGoogle Scholar
  18. 18.
    Verbeek, H.M.W., Wynn, M.T., Van der Aalst, W.M.P., Ter Hofstede, A.H.M.: Reduction Rules for Reset/Inhibitor Nets. BMP Center Report BMP-07-13, BMP-center.org (2007)Google Scholar
  19. 19.
    Van der Vlugt, S., Kleijn, J., Koutny, M.: Coverability and Inhibitor Arcs: An Example. Technical Report 1293, University of Newcastle Upon Tyne (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Guan Jun Liu
    • 1
  • Jun Sun
    • 1
  • Yang Liu
    • 2
  • Jin Song Dong
    • 3
  1. 1.ISTDSingapore University of Technology and DesignSingapore
  2. 2.Temasek LabNational University of SingaporeSingapore
  3. 3.School of ComputingNational University of SingaporeSingapore

Personalised recommendations