This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century. Second, building on the theory of functional relations in mathematics, it provides a theoretical framework where we can rigorously distinguish two pairs of concepts: Between solving a problem and verifying the solution to a problem. Between a deterministic and a non-deterministic model of computation. Third, it presents the theory of computational complexity and the difficulties in solving the P versus NP problem. Finally, it gives a complete proof that a certain decision problem in NP has an algorithmic exponential lower bound thus establishing firmly that P is different from NP. The proof presents a new way of approaching the subject: neither by entering into the unmanageable difficulties of proving this type of lower bound for the known NP-complete problems nor by entering into the difficulties regarding the properties of the many complexity classes established since the mid-1970s.

翻译：本文提出了计算复杂性问题的一个通用解决方案。首先，文章从19世纪末数学基础问题的复兴开始，对该问题进行了历史性回顾。其次，基于数学中的函数关系理论，构建了一个理论框架，在此框架下可以严格区分两对概念：解决问题的过程与验证问题解的过程，以及确定性计算模型与非确定性计算模型。第三，文章阐述了计算复杂性理论以及P与NP问题求解所面临的困难。最后，完整证明了NP中的某个判定问题具有指数级算法下界，从而明确确立了P≠NP。该证明提供了一种全新的研究思路：既不陷入为已知NP完全问题证明此类下界所面临的难以应对的困难，也不涉及自20世纪70年代中期以来建立的众多复杂性类性质方面的难题。