3 years ago

# A Proof for P =? NP Problem.

Changlin Wan

The \$\textbf{P} =? \textbf{NP}\$ problem is an important problem in contemporary mathematics and theoretical computer science. Many proofs have been proposed to this problem. This paper proposes a theoretic proof for \$\textbf{P} =? \textbf{NP}\$ problem. The central idea of this proof is a recursive definition for Turing machine (shortly TM) that accepts the encoding strings of valid TMs within any given alphabet. As the concepts "Tao", "Yin" and "Yang" described in Chinese philosopy, an infinite sequence of TM, within any given alphabet, is constructed recursively, and it is proven that the sequence includes all valid TMs, and each of them run in polynomial time. Based on these TMs, the class \textbf{D} that includes all decidable languages is defined, and then the class \$\textbf{P}\$ and \$\textbf{NP}\$ are defined. By proving \$\textbf{P} \subseteq \textbf{NP}\$ and \$\textbf{NP} \subseteq \textbf{P}\$, the result \$\textbf{P}=\textbf{NP}\$ is proven.

Publisher URL: http://arxiv.org/abs/1005.3010

DOI: arXiv:1005.3010v7

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