摘要翻译：
本文分析了随机CSP模型（即RB模型）的缩放窗口，它可以准确地识别阈值点，用$R_{cr}$或$P_{cr}$表示。对于这个模型，我们建立缩放窗口$W(n,\delta)=(r_{-}(n,\delta),r_{+}(n,\delta))$使得随机实例可满足的概率大于$1-\delta$对于$R<r_{-}(n,\delta)$而小于$\delta$对于$R>r_{+}(n,\delta)$。具体地，我们得到了如下结果$$w(n,\delta)=(r_{cr}-\theta(\frac{1}{n^{1-\epsilon}\ln n}）,\r_{cr}+\theta(\frac{1}{n\ln n}）,其中$0\leq\epsilon<1$是常数。对于另一个参数$p$也得到了类似的结果。由于模型RB生成的实例在阈值处被证明是硬的，这是第一次尝试，据我们所知，用硬实例来分析这样一个模型的缩放窗口。
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英文标题：
《On the Scaling Window of Model RB》
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作者：
Chunyan Zhao, Ke Xu, Zhiming Zheng
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最新提交年份：
2008
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分类信息：

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。
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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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。
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英文摘要：
  This paper analyzes the scaling window of a random CSP model (i.e. model RB) for which we can identify the threshold points exactly, denoted by $r_{cr}$ or $p_{cr}$. For this model, we establish the scaling window $W(n,\delta)=(r_{-}(n,\delta), r_{+}(n,\delta))$ such that the probability of a random instance being satisfiable is greater than $1-\delta$ for $r<r_{-}(n,\delta)$ and is less than $\delta$ for $r>r_{+}(n,\delta)$. Specifically, we obtain the following result $$W(n,\delta)=(r_{cr}-\Theta(\frac{1}{n^{1-\epsilon}\ln n}), \ r_{cr}+\Theta(\frac{1}{n\ln n})),$$ where $0\leq\epsilon<1$ is a constant. A similar result with respect to the other parameter $p$ is also obtained. Since the instances generated by model RB have been shown to be hard at the threshold, this is the first attempt, as far as we know, to analyze the scaling window of such a model with hard instances.
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PDF链接：
https://arxiv.org/pdf/0801.3871