While prior work established a verifier-based polynomial-time framework for NP, explicit deterministic machines for concrete NP-complete problems have remained elusive. In this paper, we construct fully specified deterministic Turing Machines (DTMs) for SAT and Subset-Sum within an improved NP verifier simulation framework. A key contribution of this work is the development of a functional implementation that bridges the gap between theoretical proofs and executable software. Our improved feasible-graph construction yields a theoretical reduction in the asymptotic polynomial degree, while enhanced edge extension mechanisms significantly improve practical execution speed. We show that these machines generate valid witnesses, extending the framework to deterministic FNP computation without increasing complexity. The complete Python implementation behaves in accordance with the predicted polynomial-time bounds, and the source code along with sample instances are available in a public online repository.

翻译：尽管先前的工作已建立了基于验证器的NP多项式时间框架，但针对具体NP完全问题的显式确定性机器仍难以实现。本文在改进的NP验证器仿真框架内，为SAT与子集和问题构建了完全指定的确定性图灵机（DTM）。本工作的核心贡献在于开发了一种功能性实现，弥合了理论证明与可执行软件之间的鸿沟。改进的可行图构造方法在理论上降低了渐近多项式度数，而增强的边扩展机制则显著提升了实际执行速度。我们证明这些机器能够生成有效证据，在未增加复杂性的前提下将框架扩展至确定性FNP计算。完整的Python实现严格符合预测的多项式时间界限，源代码及示例实例已发布于公共在线仓库。