逼近阻力的一个刻画
A Characterization of Approximation Resistance
摘要：
一个谓词f：{-1，1}^k -> {0，1}，其中ρ（f）= \frac{|f^{-1}(1)|}{2^k}，称为{ \it近似抵抗}，如果给定CSP（f）的一个近似可满足的实例，在计算上很难找到一个至少满足ρ（f）+Ω（1）分数约束的赋值。我们提出了一个完整的表征近似下的唯一游戏猜想的谓词。我们还提出了{ \it混合}线性和半定规划层次和Sherali-Adams线性规划层次的特征。在前一种情况下，特征与基于UGC的特征相吻合。这两个刻画都是关于与谓词相关的自然凸多面体上具有一定对称性的概率测度的存在性。
英文摘要：
A predicate f:{-1,1}^k -> {0,1} with ρ(f) = \frac{|f^{-1}(1)|}{2^k} is called {\it approximation resistant} if given a near-satisfiable instance of CSP(f), it is computationally hard to find an assignment that satisfies at least ρ(f)+Ω(1) fraction of the constraints. We present a complete characterization of approximation resistant predicates under the Unique Games Conjecture. We also present characterizations in the {\it mixed} linear and semi-definite programming hierarchy and the Sherali-Adams linear programming hierarchy. In the former case, the characterization coincides with the one based on UGC. Each of the two characterizations is in terms of existence of a probability measure with certain symmetry properties on a natural convex polytope associated with the predicate.
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