Computing Refined Ordering Relations with Uncertainty for Acyclic Process Models

Since the behavior is the essential characteristic of business process models, and ordering relations between execution of tasks can be used to describe the behavior of process models, we need to compute the ordering relations between tasks in process models. This computation can be used for compliance checking and querying process models based on behavior. There are three basic types of ordering relations between two events in a concurrent system, i.e., causal, conflict, and concurrency. In this paper, we refine the causal and concurrency relations with uncertainty according to whether one task is always executed with the other task in the same instance. To compute the refined ordering relations with uncertainty efficiently, we propose some rules for adjacent tasks and some transitive laws for nonadjacent tasks together with their proofs. Based on these rules and laws, we propose an algorithm to compute the refined ordering relations for acyclic process models based on unfolding technology. The algorithm has a biquadrate time to the size of complete prefix unfolding of the original model.