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)


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.


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


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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

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