Complexity of the Soundness Problem of Bounded Workflow Nets
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.
KeywordsPetri nets workflow nets workflow nets with reset arcs soundness co-NP-hardness PSPACE-hardness
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- 3.Van der Aalst, W.M.P.: Structural Characterizations of Sound Workflow Nets. Computing Science Report 96/23, Eindhoven University of Technology (1996)Google Scholar
- 9.Garey, M.R., Johnson, D.S.: Computer and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company (1976)Google Scholar
- 10.Hack, M.: Petri Net Languages. Technical Report 159. MIT (1976)Google Scholar
- 15.Ohta, A., Tsuji, K.: NP-hardness of Liveness Problem of Bounded Asymmetric Choice Net. IEICE Trans. Fundamentals E85-A, 1071–1074 (2002)Google Scholar
- 18.Verbeek, H.M.W., Wynn, M.T., Van der Aalst, W.M.P., Ter Hofstede, A.H.M.: Reduction Rules for Reset/Inhibitor Nets. BMP Center Report BMP-07-13, BMP-center.org (2007)Google Scholar
- 19.Van der Vlugt, S., Kleijn, J., Koutny, M.: Coverability and Inhibitor Arcs: An Example. Technical Report 1293, University of Newcastle Upon Tyne (2011)Google Scholar