Complexity of the soundness problem of bounded workflow nets

  • Authors:

  • Guan Jun Liu;Jun Sun;Yang Liu;Jin Song Dong

  • Affiliations:

  • ISTD, Singapore University of Technology and Design, Singapore;ISTD, Singapore University of Technology and Design, Singapore;Temasek Lab, National University of Singapore, Singapore;School of Computing, National University of Singapore, Singapore

  • Venue:
  • PETRI NETS'12 Proceedings of the 33rd international conference on Application and Theory of Petri Nets
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

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.