Grading and Calculation of Synchronic Distance in Petri Nets for Trustworthy Modeling and analyzing

Synchronization plays a crucial role in computer systems, providing support for system security, data consistency, and coordination. It contributes to the establishment and application of trust, security, and dependability in distributed systems and concurrent computing to a significant extent. This article makes innovative contributions in the field of synchronic distance in Petri net. We provide refined definitions for the hierarchical classification of synchronic levels in Petri net, proposing the concepts of absolute synchronization, strong synchronization, and extended synchronization based on different conditions. Furthermore, we propose an innovative method for calculating synchronic distance. This method can automate the calculation of synchronic distance between any two transitions using computer computation, resulting in improved accuracy and reduced errors. This novel approach provides an effective tool for system security and trustworthy modeling, as accurate synchronic distance calculations allow for better evaluation of synchronic distance between different transitions, leading to the identification of potential security vulnerabilities and design flaws, thereby enhancing the credibility of decision-making and promoting the reliability of models and analysis results. To validate the proposed method, we introduce a specific example of a Petri net with concurrency, demonstrate the practicality and effectiveness of the proposed method and algorithm through analysis of this example. Our work extends the research on Petri net synchronic distance, further advancing the understanding and exploration of this field.