Convertibility and Conversion Algorithm of Well-Structured Workflow Net to Process Tree

A workflow net is a Petri net for modeling and analyzing a workflow. A process tree has been proposed as a representational bias of a workflow net and enabled us to grasp the structure of actions routing such as sequence, choice and parallel in the workflow net. The advantage of process trees enables us to grasp the structure of action routing such as sequence, choice, and parallel in a given workflow net. Unfortunately, workflow nets are not always convertible to process trees. In this paper, we discuss the convertibility and conversion of workflow nets to process trees. We first proposed a necessary and sufficient condition on convertibility, i.e. a workflow net is convertible to a process tree iff it is acyclic, bridge-less, and well-structured. Next, based on the condition we constructed an algorithm to convert the workflow net to a process tree. Then we proposed an application of the conversion algorithm, which allows us to calculate the state number of the workflow net.