## 5 Conclusions and Future Work  
The lack of support for full-featured SQL and procedural query languages in relational databases and, in particular, the absence of consideration for provenance transformation have seriously limited the application of data provenance. This paper proposes a provenance model and explains the application of our model in actual scenarios to resolve the above limitations. Firstly, we presented a provenance representation PET-based method on where-prov and further introduced the notion of a provenance graph and provenance route. Then, we described the provenance transformation process from relational tables, fields, tuples, and values, which are helpful for understanding and analyzing the dependence and transformation relationship between data. Furthermore, the provenance model is significant for implementing a fully automated debugging and elimination system or tool.  
We also implemented our model and extended PostgreSQL to ProvPg with new features, such as database provenance information query and visualization. The implementation of ProvPg verifies the feasibility of applying our model and method and provides new implementation ideas and solutions for capturing provenance information in full-featured SQL and procedural languages. We are confident that our provenance model could be applied to specific business scenarios and make targeted optimizations in subsequent research, such as data debugging and exclusion.  
**Supplementary Materials:** The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13010064/s1](https://www.mdpi.com/article/10.3390/app13010064/s1)]([https://www.mdpi.com/article/10.3390/app13010064/s1](https://www.mdpi.com/article/10.3390/app13010064/s1)), Figure S1: The ratios of load caused by adding data provenance to PostgresSQL. In one particular test environment, a database of three sizes (1G, 4G, 10G) and 22 SQLs are used for query testing; Table S1: Runtime comparison of PostgreSQL and ProvPg on dataset with 1G, 4G, and 10G load. PG and PPG are the abbreviations of PostgreSQL and ProvPg. (millisecond); Table S2: Correlation of overhead ratio with materialized operation on a dataset with 1G, 4G, and 10G load. R1: the materialization ratio, R2: the extra cost RATIO, \(\rho\)R1, R2 IS, the Pearson's correlation coefficient of R1 and R2, the extra cost RATIO, \(\rho\)R1, R2 IS, the Pearson's correlation coefficient of R1 and R2.  
**Author Contributions:** Conceptualization, D.T. and Y.L.; methodology, D.T., Y.L. and R.Z.; software, R.Z. and Y.L.; validation, D.T., Y.L. and R.Z.; formal analysis, D.T., Y.L. and R.Z.; investigation, D.T. and Y.L.; resources, D.T.; data curation, R.Z. writing--original draft preparation, D.T. and R.Z.; writing--review and editing, D.T. and R.Z.; visualization, R.Z. and Y.L.; supervision, P.Z.; project administration, T.Z., D.T. and P.Z.; funding acquisition, D.T. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Key Laboratory of Industrial Equipment Quality Big Data, MIIT, grant number 2021-IEQBD-04.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.