## 6 Discussion  
The experimental study shows that the proposed approach can be applied in various conditions and problem domains and diverse structure of process maps. The optimization procedure enables the construction of explicit and understandable process maps with good coverage of the event log. The optimized process maps for the considered cases reveal key sequences of events and demonstrate a good reflection of the processes' nature. One of the challenging issues discovered within the study is managing cyclic meta-states as part of the model optimization procedure and further domain interpretation. The revealed complexity landscapes become highly \"rugged\" after the introduction of aggregation procedures (see Figures 9-12). This leads to the appearance of multiple local optimums. Although these optimums may be considered stable and interpretable process maps, they cover or do not cover certain field-specific states. Within the proposed approach, we focused on reaching higher interpretability of process maps from this point of view. Thus, this issue goes beyond the problem of global optimization. The presence or absence of particular meta-states should be considered from the domain-specific point of view with a further interpretation that can impose restrictions on a global optimization problem during process discovery within the proposed approach. The number of meta-states varies over the parameter space significantly (see, e.g., Figure 12(a) for the monitoring process). To analyze the structure of meta-states discovered in different areas of the parametric space, we identified the meta-states' appearance for the monitoring program case. Within a basic grid search, we discovered 15 possible combinations of meta-states (see Figure 12(b),d for a description of states). Still, the more important issues can be revealed when considering the structure of adjacent areas. In Figure 12(c), we introduce a graph structure showing the transitions between combinations by adding meta-states (e.g., edge \"+CF I HD\" means that moving from combination C14 to combination C12 is reflected in adding two cycles \"CF\" and \"HD\"--see the Figure 12(d) caption for the interpretation). Several measures can be introduced to identify the relevance of the combination to the actual process, e.g., by assessing the coverage area in parameter space or the centrality measure in the proposed graph structure. Here, one can select combinations C2, C9, C14 by their centrality and high coverage of parameter space. Moreover, C2, C9 have implicit evidence of their consistency as transitions from loose multiple meta-states with increasing complexity (see, e.g., transitions to combinations C3, C4, C5, C6, C8). Thus, in this case, the combinations can be selected to define the area for the optimization within the parametric space. Additionally, it is worth mentioning that common PM approaches focus on the most frequent traces within the event log. Still, in many cases, rare behavior may also present significant variants of the process. To tackle such issues, specific procedures may be introduced both in the internal structuring process models [63] and in the decomposition of event log data (e.g., by clustering) [41]. While the last approach may be directly combined with the proposed methods, it introduces a series of process models where meta-states may possibly be semantically connected. At the same time, internal restructuring of the process model may also be implemented as an extension of the proposed formal identification of meta-states. Considering the limitations of the proposed approach, several important issues have to be mentioned. First, the proposed optimization is based on a balance between event log coverage (fitness), process complexity, and interpretability. These criteria generally contradict each other. This leads to a complex multi-criterion optimization problem which  
Figure 13: Meta-state combination: (**a**) number of significant cycles; (**b**) covered area; (**c**) transition states; (**d**) legend (meas.