# Translating Workflow Nets to Process Trees: An Algorithmic Approach
## 5 Related Work
The RPST decomposition has been exploited in various noteworthy other studies. In [27; 28], the authors used the RPST to \"structure acyclic process models\". The core idea is to compute an RPST decomposition of a given acyclic model, which is possibly unstructured. An unstructured part of the model is recognized as a _rigid component_ in the RPST decomposition. Subsequently, the behavioral ordering relations of the rigid component are computed, and a corresponding structured process model is synthesized. Since there exist process models that do not have an equivalent well-structured representation, the aforementioned work is further extended in [29], in which the authors exploited the RPST decomposition to compute a maximally structured version of the input process model. In [30], the authors extended the notion of RPSTs for _sound free-choice WF-nets_, i.e., referred to as a WF-tree. Within a WF-Tree, certain internal vertices can be labeled as being either place-bordered, transition-bordered, or as a loop construct. As such, the authors partially annotated the RPST with behavioral information. Whereas the RPST is computed on the basis of a tree of _triconnected components_, other similar tree-based abstractions of process models have been considered as well. In [31], the authors proposed to exploit the tree of _biconnected components_ to check whether a given workflow net is sound on the basis of its structure. In particular, the authors show that it is sufficient to show that one biconnected subnet of the workflow net is not safe and sound, to conclude that the WF-net as a whole is not sound. The reductions presented in this paper, alternatively to the different works on translating process modeling formalisms into each other, bear similarity to various reduction rules established on general Petri nets. The general idea of Petri net reduction (or the opposite, expansion) is a substitution of elements of a Petri net, i.e., either by a smaller or larger newly added subnet, while preserving the behavioral properties of the net. For example, in [32], the authors proposed step-wise refinements of both transitions and places in Petri nets, while preserving liveness and boundedness properties of the Petri net. Similarly, in [33], the author proposed a set of reduction rules for Colored WF-nets, i.e., WF-nets with additional data flow semantics. In [34], the authors presented a set of reduction rules for free-choice probabilistic WF-nets, i.e., WF-nets in which transitions have an associated probability and reward. In particular, the reduction rules are proposed in order to preserve the expected reward of the workflow. Clearly, the work presented in this paper bears similarity with the different works mentioned. However, the works in the area of process model transformation are typically not defined for WF-nets, e.g., the RPST decomposition, or are more restrictive on the patterns to be replaced, e.g., the maximized unique source/sink patterns of [23]. Similarly, whereas the reduction patterns defined here do preserve the soundness of the WF-net, i.e., if the given WF-net is sound, the core of the related work in the field focuses more on the preservation of various behavioral properties.