## 7 Discussions  
The study of workflow systems necessitates a holistic approach that integrates both process data operations and persistent data operations. Existing research often focuses on only one of these aspects, leading to a fragmented understanding of data inconsistency. A primary challenge in addressing this issue lies in constructing a formal model that simultaneously captures both perspectives while also efficiently managing unbounded data when process data values are stored in the database.  
Several formal models, such as the RAW-SYS framework [32] and DB-nets [33], have been proposed to represent process execution and its interaction with persistent data. However, these models do not provide a comprehensive method for detecting data inconsistencies across both process and persistent data dimensions, nor do they specify effective handling mechanisms for unbounded data.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Model**} & \multicolumn{6}{c}{**Data Inconsistency**} \\ \cline{2-13}
**BM** & & \multicolumn{3}{c}{**WF**} & \multicolumn{3}{c}{**WFD**} & \multicolumn{3}{c}{**WFT**} & \multicolumn{3}{c}{**w.r.t. Concurrent**} & \multicolumn{3}{c}{**w.r.t. Shared**} \\  & & \multicolumn{3}{c}{**Operation**} & \multicolumn{3}{c}{**Attributes**} \\ \cline{2-13}  & **T** & **P** & **F** & **D** & **G** & **D** & **R** & **G** & **WFD** & **WFT** & **WFD** & **WFT** \\ \hline BM1 & 20 & 24 & 52 & 6 & 4 & 6 & 2 & 4 & 2 & 2 & - & 1 \\ BM2 & 19 & 17 & 41 & 7 & 8 & 7 & 2 & 8 & 1 & 1 & - & 2 \\ BM3 & 15 & 15 & 33 & 9 & 4 & 9 & 2 & 4 & 2 & 2 & - & 2 \\ BM4 & 18 & 15 & 38 & 8 & 8 & 8 & 2 & 8 & 2 & 2 & - & 1 \\ BM5 & 18 & 17 & 38 & 10 & 6 & 10 & 2 & 6 & 2 & 2 & - & 1 \\ BM6 & 18 & 15 & 39 & 10 & 10 & 10 & 2 & 10 & 2 & 2 & - & 1 \\ BM7 & 17 & 16 & 38 & 10 & 6 & 10 & 2 & 6 & 2 & 2 & - & 1 \\ BM8 & 13 & 12 & 28 & 10 & 6 & 10 & 2 & 6 & 2 & 2 & - & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Modeling data details of experiments and result.  
The WFT-net model, initially introduced in our previous work [34], provides a structured solution to these issues. First, it integrates workflow nets with relational tables, explicitly representing both control flow and persistent data, while linking them through process data. This dual-layered representation enables a more detailed analysis of inconsistencies arising from improper data operations. Second, by attaching data operations directly to transitions, WFT-nets leverage existing Petri net analysis techniques, such as graph traversal, to facilitate automated inconsistency detection. Third, as a conceptual model, WFT-nets introduce a refined data handling strategy, transforming potentially infinite data values into a manageable finite state space, thereby allowing for a more effective problem analysis.  
This work advances the capability of WFT-nets in inconsistency detection by constructing an extended reachability graph that explicitly captures all data operations associated with transition firings. A novel data refining strategy is introduced to address the limitations of previous approaches, particularly regarding inconsistencies caused by data overwrites. By systematically traversing the extended reachability graph, data inconsistencies are identified, and the proposed method's validity is confirmed through theoretical analysis. Moreover, comparative experiments with WFD-nets further demonstrate the effectiveness and efficiency of the approach.  
In summary, this study not only provides an enhanced methodology for detecting data inconsistencies in workflow systems but also contributes to the broader field of workflow and logical system modeling in computer science. The WFT-net model offers a comprehensive framework that integrates process and persistent data analysis, facilitates the detection of inconsistency errors, and improves the efficiency of unbounded data management, thereby laying the foundation for future research on workflow verification and repair strategies.