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On Generating Hierarchical Workflow Nets and their Extensions and Verifying Hierarchicality

Sroka J., Chrząstowski-Wachtel P., Hidders J.

Fundamenta Informaticae

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2015

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Vol. 141, nr 4

367--398

EN

For designing and analyzing complex workflow nets the notion of hierarchical decomposition can be essential for keeping the structure of the workflow comprehensible. In this paper we study two classes of nets: hierarchical nets and extended hierarchical nets. The first have a simple hierarchical structure and can be defined in terms of five simple refinement rules. We show that for arbitrary nets it can be easily verified if they can be constructed this way, thus confirming their good design and the properties following from it. As we prove, this can be done by performing the refinements in reverse, i.e., by contracting subnets into single nodes. It is shown that the choice of the contracted subnet does not change the final result of the process, and therefore this procedure for checking the hierarchical structure requires no back-tracking. The second class, extended hierarchical nets, is an extension of the first class where two types of extra refinements are introduced that allow to indicate (1) the synchronization between two parallel running subworkflows or (2) the transfer of a thread from one subworkflow to another one. These refinements come with natural and necessary preconditions that ensure that result is still a sound workflow net. In case (1) where we want to synchronize two actions in two subworkflows, we should convince ourselves that the subworkflows represent parallel threads which always execute together, otherwise a deadlock could easily arise. Dually, in case (2), if after the moment that a choice was made between two subworkflows we at a later point in the workflow want to allow a transfer between them, this can be done safely provided that we did not enter any thread fork in the meantime. We show that the class of extended hierarchical nets, which is defined by adding these two additional types of refinement, is a proper superset of the hierarchical nets, but still all such nets exhibit the correctness property of *-soundness. We do this by showing that the class is a proper subset of the AND-OR nets which were in earlier work shown to have this property.

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Time Distribution in Structural Workflow Nets

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

Fundamenta Informaticae

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2008

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Vol. 85, nr 1-4

67-87

EN

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.

3

Determining Sound Markings in Structured Nets

Chrząstowski-Wachtel P.

Fundamenta Informaticae

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2006

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Vol. 72, nr 1-3

65-79

EN

When we model workflows with Petri nets, we call a workflow net sound, if it neither makes any transition dead nor it produces trash tokens in such a way that for every input token exactly one token appears eventually on the output place. We assume that the initial marking consists always of one token on the input place. However, sometimes it is necessary to take into account arbitrary markings, for instance when we make a recovery from an unexpected situation during the workflow execution. An arbitrary marking is sound if it eventually produces exactly one output token without the possibility to leave any trash tokens. The paper addresses the problem of determining the proper control recovery, when unexpected situation arises, and we must detour from the normal execution. When we create an arbitrary control state during the recovery, it is easy to overlook some consequences and create either trash tokens or a deadlock in the future. The problem of determining if a given marking is sound is addressed in the paper in the context of structured nets. The presented linear solution is a necessary and sufficient condition for soundness of markings in structured nets.