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Some Complexity Results for the Soundness Problem of Workflow Nets
PrePrint
ISSN: 1939-1374
GuanJun Liu, Singapore University of Technology and Design, Singapore
Workflow nets (WF-nets) are widely used to model and verify the business process management systems and composite web services. The (weak) soundness of WF-nets is an important criterion for the correctness of these systems. This paper focuses on the complexity of solving the (weak) soundness problem. Aalst \emph{et. al.} have proven that the (weak) soundness problem is decidable. Our previous work has proven that the soundness problem for bounded WF-nets is PSPACE-complete. This paper shows that the weak soundness problem for bounded WF-nets is also PSPACE-complete. Aalst \emph{et. al.} has proven that the soundness problem is polynomially solvable for free-choice WF-nets (FCWF-nets). This paper discovers that the weak soundness problem is equivalent to the soundness problem for FCWF-nets. Therefore, the weak soundness problem for FCWF-nets is also polynomially solvable. Unfortunately, many composite web services are not modeled by FCWF-nets. Lots of them can be modeled by asymmetric-choice WF-nets (ACWF-nets). This paper proves that the soundness problem is co-NP-hard for ACWF-nets even when they are 3-bounded. Additionally, this paper proves that the $k$-soundness problem is equivalent to the weak soundness problem for WF-nets, which implies that the $k$-soundness problem for bounded WF-nets is also PSPACE-complete.
Index Terms:
Formalization of Services Composition,Services Computing,Business Process Management and Integration,General,Business Process Modeling,Services Composition,General
Citation:
GuanJun Liu, "Some Complexity Results for the Soundness Problem of Workflow Nets," IEEE Transactions on Services Computing, 18 June 2013. IEEE computer Society Digital Library. IEEE Computer Society, <http://doi.ieeecomputersociety.org/10.1109/TSC.2013.36>
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