Skip to main content
Book cover

Transactions on Petri Nets and Other Models of Concurrency IX pp 1–18Cite as

Decidability of \(k\)-Soundness for Workflow Nets with an Unbounded Resource

Part of the Lecture Notes in Computer Science book series (TOPNOC,volume 8910)

Abstract

A resource workflow net (RWF-net) is a workflow net, supplied with an additional set of initially marked resource places. Resources can be consumed and/or produced by transitions. Neither the intermediate nor final resource markings are constrained, hence a net can have an infinite number of different reachable states.

An RWF-net with \(k\) tokens in the initial place and a certain number of resource tokens in resource places is called \(k\)-sound if it properly terminates with \(k\) tokens in the final place and, moreover, adding any extra initial resource does not violate its proper termination. An unmarked RWF-net is \(k\)-sound if it is \(k\)-sound for some initial resource. In this paper we prove the decidability of both marked and unmarked \(k\)-soundness for a restricted class of RWF-nets with a single unbounded resource place (1-dim RWF-nets). We present an algorithm for computing the minimal \(k\)-sound resource for a given sound 1-dim RWF-net.

Keywords

  • Petri nets
  • Workflow
  • Soundness
  • Modeling
  • Verification

This work is supported by the Basic Research Program of the National Research University Higher School of Economics.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-662-45730-6_1
  • Chapter length: 18 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   39.99
Price excludes VAT (USA)
  • ISBN: 978-3-662-45730-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   54.99
Price excludes VAT (USA)
Learn about institutional subscriptions
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

References

  1. van der Aalst, W.M.P.: The application of Petri Nets to workflow management. J. Circuits Syst. Comput. 8(1), 21–66 (1998)

    CrossRef  Google Scholar 

  2. van der Aalst, W.M.P., van Hee, K.M.: Workflow Management: Models. MIT Press, Methods and Systems (2002)

    Google Scholar 

  3. 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 Comput. 23(3), 333–363 (2011)

    CrossRef  MATH  Google Scholar 

  4. Abdulla, P.A., Čerans, K.: Simulation is decidable for one-counter nets. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 253–268. Springer, Heidelberg (1998)

    CrossRef  Google Scholar 

  5. Barkaoui, K., Petrucci, L.: Structural analysis of workflow nets with shared resources. In: van der Aalst, W.M.P., Michelis, G., Ellis, C.A. (eds.) Proceedings of Workflow Management: Net-based Concepts, Models, Techniques and Tools (WFM’98). Computing Science Reports, vol. 98/7, pp. 82–95. Eindhoven University of Technology, Eindhoven (1998)

    Google Scholar 

  6. Barkaoui, K., Ben Ayed, R., Sbaï, Z.: Workflow soundness verification based on structure theory of Petri Nets. Int. J. Comput. Inf. Sci. 5(1), 51–61 (2007)

    Google Scholar 

  7. Bashkin, V.A.: Formalization of semantics of systems with unreliable agents by means of nets of active resources. Programm. Comput. Softw. 36(4), 187–196 (2010)

    CrossRef  MATH  MathSciNet  Google Scholar 

  8. Bashkin, V.A.: Modular nets of active resources. Automatic Control Comput. Sci. 46(1), 1–11 (2012)

    CrossRef  Google Scholar 

  9. Bashkin, V.A., Lomazova, I.A.: Petri Nets and resource bisimulation. Fundamenta Informaticae 55(2), 101–114 (2003)

    MATH  MathSciNet  Google Scholar 

  10. Bashkin, V.A., Lomazova, I.A.: Resource similarities in Petri Net models of distributed systems. In: Malyshkin, V.E. (ed.) PaCT 2003. LNCS, vol. 2763, pp. 35–48. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  11. Bashkin, V.A., Lomazova, I.A.: Similarity of generalized resources in Petri Nets. In: Malyshkin, V.E. (ed.) PaCT 2005. LNCS, vol. 3606, pp. 27–41. Springer, Heidelberg (2005)

    CrossRef  Google Scholar 

  12. Bashkin, V.A., Lomazova, I.A.: Resource Equivalence in Workflow Nets. In: Proceedings of CS&P’2006 on Concurrency, Specification and Programming, vol. 1., pp. 80–91. Humboldt-Universitat zu Berlin, Berlin (2006)

    Google Scholar 

  13. Bashkin, V.A., Lomazova, I.A.: Resource driven automata nets. Fundamenta Informaticae 109(3), 223–236 (2011)

    MATH  MathSciNet  Google Scholar 

  14. Bashkin, V.A., Lomazova, I.A.: Modelling multiagent systems with the help of generalized nets of active resources. Cybern. Syst. Anal. 47(2), 202–209 (2011)

    CrossRef  MATH  MathSciNet  Google Scholar 

  15. Bashkin, V.A., Lomazova, I.A.: Cellular resource-driven automata. Fundamenta Informaticae 120(3–4), 243–257 (2012)

    MATH  MathSciNet  Google Scholar 

  16. Bashkin, V.A., Lomazova, I.A.: Soundness of Workflow Nets with an Unbounded Resource is Decidable. In: Joint Proceedings of PNSE’13 and ModBE’13. CEUR Workshop Proceedings, vol. 989, pp. 61–75. CEUR-WS.org (2013)

    Google Scholar 

  17. Dehnert, J., Rittgen, P.: Relaxed soundness of business processes. In: Dittrich, K.R., Geppert, A., Norrie, M. (eds.) CAiSE 2001. LNCS, vol. 2068, pp. 157–170. Springer, Heidelberg (2001)

    CrossRef  Google Scholar 

  18. 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)

    CrossRef  Google Scholar 

  19. van Hee, K.M., Serebrenik, A., Sidorova, N., Voorhoeve, M.: Soundness of resource-constrained workflow nets. In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 250–267. Springer, Heidelberg (2005)

    CrossRef  Google Scholar 

  20. van Hee, K., Oanea, O., Serebrenik, A., Sidorova, N., Voorhoeve, M., Lomazova, I.A.: Checking properties of adaptive workflow nets. Fundamenta Informaticae 79(3–4), 347–362 (2007)

    MATH  MathSciNet  Google Scholar 

  21. Hopcroft, J.E., Pansiot, J.J.: On the reachability problem for 5-dimensional vector addition systems. Theor. Comput. Sci. 8, 135–159 (1979)

    CrossRef  MATH  MathSciNet  Google Scholar 

  22. Lomazova, I.A., Romanov, I.V.: Analyzing compatibility of services via resource conformance. Fundamenta Informaticae 128(1–2), 129–141 (2013)

    MATH  MathSciNet  Google Scholar 

  23. Puhlmann, F., Weske, M.: Interaction soundness for service orchestrations. In: Dan, A., Lamersdorf, W. (eds.) ICSOC 2006. LNCS, vol. 4294, pp. 302–313. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  24. Sidorova, N., Stahl, C.: Soundness for resource-contrained workflow nets is decidable. IEEE Trans. Syst. Man Cybern. Syst. 43(3), 724–729 (2013)

    CrossRef  Google Scholar 

  25. Tiplea, F.L., Marinescu, D.C.: Structural soundness of workflow nets is decidable. Inf. Process. Lett. 96(2), 54–58 (2005)

    CrossRef  MATH  MathSciNet  Google Scholar 

  26. van der Toorn, R.A.: Component-based software design with Petri Nets: An approach based on inheritance of behavior. Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yaroslavl State University, Yaroslavl, 150000, Russia

    Vladimir A. Bashkin

  2. National Research University Higher School of Economics (HSE), Moscow, 101000, Russia

    Irina A. Lomazova

Authors
  1. Vladimir A. Bashkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Irina A. Lomazova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irina A. Lomazova .

Editor information

Editors and Affiliations

  1. School of Computing Science, Newcastle University, Newcastle upon Tyne, United Kingdom

    Maciej Koutny

  2. École Normale Supérieure de Cachan, Cachan, France

    Serge Haddad

  3. Newcastle University, Newcastle upon Tyne, United Kingdom

    Alex Yakovlev

Rights and permissions

Reprints and Permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bashkin, V.A., Lomazova, I.A. (2014). Decidability of \(k\)-Soundness for Workflow Nets with an Unbounded Resource. In: Koutny, M., Haddad, S., Yakovlev, A. (eds) Transactions on Petri Nets and Other Models of Concurrency IX. Lecture Notes in Computer Science(), vol 8910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45730-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-45730-6_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-45729-0

  • Online ISBN: 978-3-662-45730-6

  • eBook Packages: Computer ScienceComputer Science (R0)