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Complexity of the Soundness Problem of Workflow Nets

Liu G. J., Sun J., Liu Y., Dong J. S.

Fundamenta Informaticae

2014

Vol. 131, nr 1

81--101

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.

Learning Workflow Petri Nets

Esparza J., Leucker M., Schlund M.

Fundamenta Informaticae

2011

Vol. 113, nr 3/4

205-228

Workflow mining is the task of automatically producing a workflow model from a set of event logs recording sequences of workflow events; each sequence corresponds to a use case or workflow instance. Formal approaches to workflow mining assume that the event log is complete (contains enough information to infer the workflow) which is often not the case. We present a learning approach that relaxes this assumption: if the event log is incomplete, our learning algorithm automatically derives queries about the executability of some event sequences. If a teacher answers these queries, the algorithm is guaranteed to terminate with a correct model. We provide matching upper and lower bounds on the number of queries required by the algorithm, and report on the application of an implementation to some examples.

Time Distribution in Structural Workflow Nets

Chrząstowski-Wachtel P., Findeisen P., Wolny G.

Fundamenta Informaticae

2008

Vol. 85, nr 1-4

67-87

Workflows with transition execution times having exponential distributions are considered. The aim is to determine the overall execution time without looking into the reachability space and its analysis using Markov processes. We concentrate on the so called structural workflows, which are represented with Petri nets constructed by means of specific refinement rules. With each refinement rule (sequence, choice, parallelization, loop) we associate formulas which allow to compute the overall execution time distribution. The class of exponential distributions is too narrow to keep the result within itself. We analyze the so called exponential polynomials, generalizing exponential distributions. They are closed under SUM and MAX functions. This closure property combined with the knowledge of refinements history enables us to find the requested formulas.