# Probabilistic Model Checking GitHub Repositories for Software Project Analysis
## 6 Conclusions  
GitHub serves as a platform where developers contribute to projects, collaborate, and shape progress. GitHub encourages collaboration in software development, and contributions are made through specific actions or commands. Data on these activities accumulate over time, and time series analysis can provide insights into the dynamics of open-source development. Unlike popular methods such as K-means clustering or LSTM networks that have been used in previous time series analyses of GitHub, we used DTMC and pCTL for model checking. By doing so, we aimed to analyze the probability of events in the development process and their temporal dynamics by modeling the flow of activity data rather than predicting the future. In particular, the explicit modeling of state transitions and probabilities with DTMC enabled a transparent understanding of sequential features while overcoming the limitations of previous approaches. pCTL also allows us to design different queries for the aspects we want to know about, so we can obtain quantitative numbers by generating different queries and performing model checking beyond what we presented in this study.  
We aimed to demonstrate the feasibility and scalability of the proposed method through a case study on five repositories. Analysis of the model checking results shed light on several key factors affecting the overall project dynamics. We were able to explore the long-term probability of various activities occurring over time and make observations about the participation and behavioral patterns of contributors. These findings can potentially help project managers optimize team dynamics and resource allocation. For example, analyzing the level of project activity can help gauge the speed of a team, and individual analysis can provide useful insights for managing team members based on their characteristics.  
In conclusion, our analysis provides valuable insights into the characteristics of GitHub repositories, branch management, and contributor behavior. We expect that our findings can provide useful perspectives for project managers and contributors to understand and improve the collaborative software development process. In the future, we plan to apply this approach to larger open-source projects to identify trends among contributors on the unique characteristics of repositories.  
Conceptualization, S.J., R.K. and G.K.; methodology, S.J.; software, S.J. and R.K.; validation, R.K. and G.K.; formal analysis, S.J. and G.K.; writing--original draft preparation, S.J. and R.K.; writing--review and editing, R.K. and G.K.; visualization, S.J.; supervision, G.K. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) (No. 2021-0-00122, Safety Analysis and Verification Tool Technology Development for High Safety Software Development).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest:** The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.