关于RB模型的尺度窗口
On the Scaling Window of Model RB
摘要：
本文分析了随机CSP模型（即RB模型）的尺度窗口，用$r_{cr}$或$p_{cr}$表示该窗口的阈值点。对于这个模型，我们建立了缩放窗口$W(n,δ)=(r_{-}(n,δ), r_{+}(n,δ))$，使得随机实例可满足的概率对于$r<r_{-}(n,δ)$大于$1-δ$，对于$r>r_{+}(n,δ)$小于$δ$。具体地说，我们得到以下结果$$W(n,δ)=(r_{cr}-Θ(\frac{1}{n^{1-ε}\ln n}), \ r_{cr}+Θ(\frac{1}{n\ln n})),$$，其中$0\leqε<1$是常数。关于另一个参数$p$也获得了类似的结果。由于模型RB生成的实例在阈值处是硬的，这是第一次尝试，据我们所知，分析具有硬实例的这种模型的缩放窗口。
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 $W(n,δ)=(r_{-}(n,δ), r_{+}(n,δ))$ such that the probability of a random instance being satisfiable is greater than $1-δ$ for $r<r_{-}(n,δ)$ and is less than $δ$ for $r>r_{+}(n,δ)$. Specifically, we obtain the following result $$W(n,δ)=(r_{cr}-Θ(\frac{1}{n^{1-ε}\ln n}), \ r_{cr}+Θ(\frac{1}{n\ln n})),$$ where $0\leqε<1$ 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.
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。
