Complexity of the Soundness Problem of Workflow Nets

  • Authors:

  • GuanJun Liu;Jun Sun;Yang Liu;JinSong Dong

  • Affiliations:

  • Department of Computer Science and Technology, Tongji University, Shanghai 201804, China. liugj1116@gmail.com;ISTD, Singapore University of Technology and Design, Singapore 138682, Singapore. sunjun@sutd.edu.sg;School of Computer Engineering, Nanyang Technological University, Singapore 639798, Singapore. yangliu@ntu.edu.sg;School of Computing, National University of Singapore, Singapore 117417, Singapore. dongjs@comp.nus.edu.sg

  • Venue:
  • Fundamenta Informaticae - Application and Theory of Petri Nets and Concurrency, 2012
  • Year:
  • 2014

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Abstract

Classical workflow nets WF-nets for short are an important subclass of Petri nets that are widely used to model and analyze workflow systems. Soundness is a crucial property of workflow systems and guarantees that these systems are deadlock-free and bounded. Aalst et al. proved that the soundness problem is decidable for WF-nets and can be polynomially solvable for free-choice WF-nets. This paper proves that the soundness problem is PSPACE-hard for WF-nets. Furthermore, it is proven that the soundness problem is PSPACE-complete for bounded WF-nets. Based on the above conclusion, it is derived that the soundness problem is also PSPACE-complete for bounded WF-nets with reset or inhibitor arcs ReWF-nets and InWF-nets for short, resp.. ReWF-and InWF-nets are two extensions to WF-nets and their soundness problems were proven by Aalst et al. to be undecidable. Additionally, we prove that the soundness problem is co-NP-hard for asymmetric-choice WF-nets that are a larger class and can model more cases of interaction and resource allocation than free-choice ones.