$\ ext{FP}^\ ext{NP}$ 与 #P 关于 #EO 的二分类定理

Constraint Satisfaction Problem Dichotomy for Finite Templates: a Proof Via Consistency Checks

One of the central problems in the study of parametrized constraint satisfaction problems is the Dichotomy Conjecture by T. Feder and M. Vardi stating that the constraint satisfaction problem (CSP) over a fixed, finite constraint language is either solvable in polynomial time or \textsc{NP}-complete. The conjecture was verified in certain special cases (domains with a relatively small number of elements, constraint languages containing all unary relations, etc.) In this article, we present a proof of the Dichotomy Conjecture via local consistency and AF- consistency checks. In fact, we show th…

基于拟多态性视角的欧拉定向计数的线性规划算法

An LP Algorithm for Counting Eulerian Orientations Through the Lens of Quasi-polymorphism

本文针对带权欧拉定向计数的FP^NP侧情况，提出基于线性规划松弛的多项式时间算法，解决其是否属于FP的问题，得到完整的FP与#P二分结果。

对林氏论文《论 $\text{NP}$ 与 $\text{coNP}$ 及 Frege 系统》的批判

A Critique of Lin's "On $\text{NP}$ versus $\text{coNP}$ and Frege Systems"

本文批判林氏关于 NP≠coNP 的证明，指出其构造的识别语言 L_d 的非确定性图灵机存在缺陷，并证明 L_d 不属于 NP，从而表明其结论及相关结果均未成立。

受限CSP与F-free有向图算法

Restricted CSPs and F-free Digraph Algorithmics

本文研究输入受限为$\vec{\mathbb P}_k$-free有向图时，有向图同态问题CSP$({\mathbb H})$的P与NP完全二分类，证明NP完全性在$\vec{\mathbb P}_N$-子图-free下保持，并引入受限CSP及其二分类。

All or nothing: toward a promise problem dichotomy for constraint problems

A finite constraint language $\mathscr{R}$ is a finite set of relations over some finite domain $A$. We show that intractability of the constraint satisfaction problem $\operatorname{CSP}(\mathscr{R})$ can, in all known cases, be replaced by an infinite hierarchy of intractable promise problems of increasingly disparate promise conditions: where instances are guaranteed to either have no solutions at all, or to be $k$-robustly satisfiable (for any fixed $k$), meaning that every "reasonable" partial instantiation on~$k$ variables extends to a solution. For example, subject to the assumption $\t…

Two theorems about the P versus NP problem

Two theorems about the P versus NP problem be proved in this article (1) There exists a language $L$, that the statement $L \in \textbf{P}$ is independent of ZFC. (2) There exists a language $L \in \textbf{NP}$, for any polynomial time deterministic Turing machine $M$, we cannot prove $L$ is decidable on $M$.

The P versus NP Problem

Removed by arXiv administration. This article was plagiarized directly from Stephen Cook's description of the problem for the Clay Mathematics Institute. See http://gauss.claymath.org:8888/millennium/P_vs_NP/pvsnp.pdf for the original text.

多轮流式处理CSPs的二元定理

A Dichotomy Theorem for Multi-Pass Streaming CSPs

本文研究了多轮流式处理CSPs的二元定理，提出了一种常数轮次的随机流式算法，以及证明了任何解决特定CSPs问题的算法必须使用Ω(n^{1/3}/p)空间。

Termwise versus globally stoquastic local Hamiltonians: questions of complexity and sign-curing

We elucidate the distinction between global and termwise stoquasticity for local Hamiltonians and prove several complexity results. We show that the stoquastic local Hamiltonian problem is $\textbf{StoqMA}$-complete even for globally stoquastic Hamiltonians. We study the complexity of deciding whether a local Hamiltonian is globally stoquastic or not. In particular, we prove $\textbf{coNP}$-hardness of deciding global stoquasticity in a fixed basis and $Σ_2^p$-hardness of deciding global stoquasticity under single-qubit transformations. As a last result, we expand the class of sign-curing tran…