Title: PBFD and PDFD: Formally Defined and Verified Methodologies and Empirical Evaluation for Scalable Full-Stack Software Engineering Show Chinese title

Title: PBFD 和 PDFD：形式化定义和验证的方法论及可扩展全栈软件工程的实证评估

Abstract: This paper introduces Primary Breadth-First Development (PBFD) and Primary Depth-First Development (PDFD), two formally defined and verified methodologies for scalable, industrial-grade full-stack software engineering. These approaches bridge a longstanding gap between formal methods and real-world development practice by enforcing structural correctness through graph-theoretic modeling. Unlike prior graph-based approaches, PBFD and PDFD operate over layered directed graphs and are formalized using unified state machines and Communicating Sequential Processes (CSP) to ensure critical properties, including bounded-refinement termination and structural completeness. To coordinate hierarchical data at scale, we propose Three-Level Encapsulation (TLE) - a novel, bitmask-based encoding scheme that delivers provably constant-time updates. TLE's formal guarantees underpin PBFD's industrial-scale performance and scalability. PBFD was empirically validated through an eight-year enterprise deployment, demonstrating over 20x faster development than Salesforce OmniScript and 7-8x faster query performance compared to conventional relational models. Additionally, both methodologies are supported by open-source MVPs, with PDFD's implementation conclusively demonstrating its correctness-first design principles. Together, PBFD and PDFD establish a reproducible, transparent framework that integrates formal verification into practical software development. All formal specifications, MVPs, and datasets are publicly available to foster academic research and industrial-grade adoption. Show Chinese abstract

Abstract: 本文介绍了初级广度优先开发（PBFD）和初级深度优先开发（PDFD），这两种是形式化定义和验证的方法，用于可扩展的工业级全栈软件工程。 这些方法通过图论建模强制结构正确性，弥合了形式化方法与现实开发实践之间长期存在的差距。 与之前基于图的方法不同，PBFD和PDFD作用于分层有向图，并使用统一状态机和通信顺序进程（CSP）进行形式化，以确保关键属性，包括有界细化终止和结构完整性。 为了协调大规模的分层数据，我们提出了三层封装（TLE）——一种新颖的基于位掩码的编码方案，能够实现可证明的常数时间更新。 TLE的形式保证支撑了PBFD的工业级性能和可扩展性。 PBFD通过八年的企业部署进行了实证验证，显示其开发速度比Salesforce OmniScript快20倍以上，查询性能比传统关系模型快7-8倍。 此外，两种方法都得到了开源MVP的支持，PDFD的实现明确证明了其以正确性为先的设计原则。 总之，PBFD和PDFD建立了一个可重复、透明的框架，将形式化验证整合到实际软件开发中。 所有形式化规范、MVP和数据集均可公开获取，以促进学术研究和工业级应用。