Representing Block-structured Process Models as Order Matrices: Basic Concepts, Formal Properties, Algorithms

In various cases we need to transform a process model into a matrix representation for further analysis. In this paper, we introduce the notion of Order Matrix, which enables unique representation of block-structured process models. We present algorithms for transforming a block-structured process model into a corresponding order matrix and vice verse. We then prove that such order matrix constitutes a unique representation of a block-structured process model; i.e., if we transform a process model into an order matrix, and then transform this matrix back into a process model, the two process models are trace equivalent; i.e., they show same behavior. Finally, we analyze algebraic properties of order matrices.