摘要翻译：
本文研究了加权$D$-CNF可满足性问题（加权$D$-SAT)的随机实例，这是一个一般的W[1]-完全问题。该问题的一个随机实例包括一个固定参数$k$和一个随机的$d$-CNF公式$\weicnf{n}{p}{k,d}$,生成如下：对于$d$变量的每个子集，以$p$的概率，从至少包含一个否定字面的$2^d-1$子句中均匀随机地选择$d$变量上的子句。我们证明了加权$D$-SAT的随机实例可以在$O(k^2n+n^{O(1)}）$-时间内以高概率求解，表明在这种实例分布下，加权$D$-SAT的典型实例是固定参数可处理的。该结果也适用于模型$\weicnf{n}{p}{k,d}(d')$中禁止包含小于$d'(1<d'<d)$否定文字的子句的随机实例，以及在随机模型参数$p(n)$的特定范围内加权$d$-SAT的重整化（小型化）版本的随机实例。这与我们以前关于$\weicnf{n}{p}{k,d}$不可满足实例的阈值行为和分辨复杂度的结果一起，提供了加权$d$-SAT随机实例典型情形行为的几乎完整的刻画。
---
英文标题：
《A Fixed-Parameter Algorithm for Random Instances of Weighted d-CNF
  Satisfiability》
---
作者：
Yong Gao
---
最新提交年份：
2008
---
分类信息：

一级分类：Computer Science        计算机科学
二级分类：Data Structures and Algorithms        数据结构与算法
分类描述：Covers data structures and analysis of algorithms. Roughly includes material in ACM Subject Classes E.1, E.2, F.2.1, and F.2.2.
涵盖数据结构和算法分析。大致包括ACM学科类E.1、E.2、F.2.1和F.2.2中的材料。
--
一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
--
一级分类：Computer Science        计算机科学
二级分类：Computational Complexity        计算复杂度
分类描述：Covers models of computation, complexity classes, structural complexity, complexity tradeoffs, upper and lower bounds. Roughly includes material in ACM Subject Classes F.1 (computation by abstract devices), F.2.3 (tradeoffs among complexity measures), and F.4.3 (formal languages), although some material in formal languages may be more appropriate for Logic in Computer Science. Some material in F.2.1 and F.2.2, may also be appropriate here, but is more likely to have Data Structures and Algorithms as the primary subject area.
涵盖计算模型，复杂度类别，结构复杂度，复杂度折衷，上限和下限。大致包括ACM学科类F.1（抽象设备的计算）、F.2.3（复杂性度量之间的权衡）和F.4.3（形式语言）中的材料，尽管形式语言中的一些材料可能更适合于计算机科学中的逻辑。在F.2.1和F.2.2中的一些材料可能也适用于这里，但更有可能以数据结构和算法作为主要主题领域。
--

---
英文摘要：
  We study random instances of the weighted $d$-CNF satisfiability problem (WEIGHTED $d$-SAT), a generic W[1]-complete problem. A random instance of the problem consists of a fixed parameter $k$ and a random $d$-CNF formula $\weicnf{n}{p}{k, d}$ generated as follows: for each subset of $d$ variables and with probability $p$, a clause over the $d$ variables is selected uniformly at random from among the $2^d - 1$ clauses that contain at least one negated literals.   We show that random instances of WEIGHTED $d$-SAT can be solved in $O(k^2n + n^{O(1)})$-time with high probability, indicating that typical instances of WEIGHTED $d$-SAT under this instance distribution are fixed-parameter tractable. The result also hold for random instances from the model $\weicnf{n}{p}{k,d}(d')$ where clauses containing less than $d' (1 < d' < d)$ negated literals are forbidden, and for random instances of the renormalized (miniaturized) version of WEIGHTED $d$-SAT in certain range of the random model's parameter $p(n)$. This, together with our previous results on the threshold behavior and the resolution complexity of unsatisfiable instances of $\weicnf{n}{p}{k, d}$, provides an almost complete characterization of the typical-case behavior of random instances of WEIGHTED $d$-SAT.
---
PDF链接：
https://arxiv.org/pdf/0806.4652