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 \textsc{SAT} and \textsc{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 genuine reduction in the asymptotic polynomial degree, while optimized edge-extension mechanisms significantly improve practical execution speed. We show that these machines generate valid witnesses, extending the framework to deterministic \textsc{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：尽管先前的研究已为NP问题建立了基于验证器的多项式时间框架，但针对具体NP完全问题的显式确定性机器仍然难以实现。本文在改进的NP验证器模拟框架内，为\textsc{SAT}和\textsc{Subset-Sum}问题构建了完全确定的图灵机（DTMs）。本工作的一个关键贡献是开发了功能性实现，弥合了理论证明与可执行软件之间的鸿沟。我们改进的可行图构造方法真正降低了渐近多项式次数，而优化的边扩展机制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见证，从而在不增加复杂度的前提下将框架扩展至确定性\textsc{FNP}计算。完整的Python实现符合预测的多项式时间边界，源代码及示例实例已公开于在线代码仓库。