置换群计数技术的一个推广（多项式族的崩溃：$\mathbf{NP = P}$）
An Extension of the Permutation Group Enumeration Technique (Collapse of the Polynomial Hierarchy: $\mathbf{NP = P}$)
摘要：
本文的判别结果是二部图中所有潜在完美匹配的一个$\mathbf{P}$ -时间可划分性。这种划分是由潜在完美匹配中的缺失边引起的一组等价类。我们捕捉到的行为，这些丢失的边缘在多项式有界表示的指数许多完美匹配的图论结构，称为MinSet序列，其中MinSet是一个P-时间可重结构来自图论对应的生成集的对称群。这导致了所有类的多项式有界生成集，使得在多项式时间内枚举完美匹配成为可能。这个$\mathbf{\#P}$ -完全问题的顺序时间复杂度是$O(n^{45}\log n)$ .因此，我们证明了一个结果，甚至更令人惊讶的$\mathbf{NP = P}$，即$\mathbf{\#P}=\mathbf{FP}$，其中$\mathbf{FP}$是一类功能，$f: \{0, 1\}^* \rightarrow \mathbb{N} $，计算在多项式时间上的确定性模型的计算。
英文摘要：
The distinguishing result of this paper is a $\mathbf{P}$-time enumerable partition of all the potential perfect matchings in a bipartite graph. This partition is a set of equivalence classes induced by the missing edges in the potential perfect matchings. We capture the behavior of these missing edges in a polynomially bounded representation of the exponentially many perfect matchings by a graph theoretic structure, called MinSet Sequence, where MinSet is a P-time enumerable structure derived from a graph theoretic counterpart of a generating set of the symmetric group. This leads to a polynomially bounded generating set of all the classes, enabling the enumeration of perfect matchings in polynomial time. The sequential time complexity of this $\mathbf{\#P}$-complete problem is shown to be $O(n^{45}\log n)$. And thus we prove a result even more surprising than $\mathbf{NP = P}$, that is, $\mathbf{\#P}=\mathbf{FP}$, where $\mathbf{FP}$ is the class of functions, $f: \{0, 1\}^* \rightarrow \mathbb{N} $, computable in polynomial time on a deterministic model of computation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
