The Difficulty of Replacing an Inclusive OR-Join

Some popular modeling languages for business processes, e.g., BPMN, contain inclusive OR-joins (IOR-joins), but others, e.g., Petri nets, do not. Various scenarios in Business Process Management require, or benefit from, translating a process model from one language to another. This paper studies whether the control flow of a process containing IOR-joins can be translated into a control flow without IOR-joins. First we characterize which IOR-joins can be replaced locally and define a local replacement for each replaceable IOR-join. Then, we present examples that cannot be locally replaced but have a more general translation. We give a non-local replacement technique, together with its condition of applicability, which runs in polynomial time. Finally, we show that there exist simple process models with an IOR-join that cannot be replaced – in the sense that its synchronization behavior cannot be obtained by any combination of AND and XOR gateways. The proof reveals an intrinsic limitation on the replaceability of IOR-joins and hence the translatability of BPMN-like control flow into Petri nets.

This technical report is the extended version of a conference publication that appears in "Business Process Management", Proc. 10th Int'l Conf. on Business Process Management "BPM," Talinn, Estonia, Lecture Notes in Computer Science, vol. 7481 (Springer, September 2012), pp.156-171