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Abstract. The Business Process Modeling Notation (BPMN) is an emerging standard for capturing business processes. Like its predecessors, BPMN lacks a formal semantics and many of its features are subject to interpretation. One construct of BPMN that has an ambiguous semantics is the OR-join. Several formal semantics of this construct have been proposed for similar languages such as EPCs and YAWL. However, these existing semantics are computationally expensive. This paper formulates a semantics of the OR-join in BPMN for which enablement of an OR-join in a process model can be evaluated in quadratic time in terms of the total number of elements in the model. This complexity can be reduced down to linear-time after materializing a quadratic-sized data structure at design-time. The paper also shows how to efficiently detect the enablement of an OR-join incrementally as the execution of a process instance unfolds.

In this paper, we report on our experiences integrating OCL evaluation support in an industrial-strength (meta-)modeling infrastructure. We focus on the approach taken to improve efficiency through what we call impact analysis of model changes to decrease the number of necessary (re-)evaluations. We show how requirements derived from application scenarios have led to design decisions that depart from or resp. extend solutions found in (academic) literature. 4 SAP and SAP NetWeaver are trademarks or registered trademarks of SAP AG in Germany and in several other countries.

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