Representation of Dynamic Basic Block in Software Evolution Using Incidence Matrix

Software evolution is a continuous process that transforms changing user requirements into improved software systems. Establishing a clear and well-structured development process is widely recognized as an effective means to enhance software maintainability, quality, and productivity. Tailoring software processes from existing process patterns and standards is essential for improving process performance, ensuring product quality, reducing development risks, and minimizing rework. Despite its importance, current research lacks a systematic and formally grounded method for tailoring software evolution processes. In this paper, we propose a structured approach based on Petri Net (PN) theory to address this limitation. There are four fundamental process constructs: sequence, concurrency, selection, and iteration are identified as basic building blocks for modeling software evolution processes. Using these constructs, four tailoring operations, namely adding, deleting, splitting, and merging, are formally defined. We study on the scalable process composition, matrix-based representations of Petri Nets (PNs) are employed. Incidence and related matrices provide a concise and mathematically tractable representation of both place/transition nets and restricted PNs, enabling the identification of essential structural properties of software processes. Also, we prove the reachability analysis and firing rules are utilized to derive a mathematical behavioral notation that captures binary relationships between input and output variables. This notation facilitates precise analysis of dynamic behavior for systematic software process tailoring.