SIAM Journal on Computing, Ahead of Print.
We show that for constraint satisfaction problems (CSPs), weakly exponential size linear programming relaxations are as powerful as the explicit linear program described by $n^{\Omega(1)}$-rounds of the Sherali--Adams linear programming hierarchy. Combining with the known lower bounds on the Sherali--Adams hierarchy, we obtain subexponential size lower bounds for linear programming relaxations that beat random guessing for many CSPs such as MAX-CUT and MAX-3SAT. This is a nearly exponential improvement over previous results; previously, it was only known that linear programs of size $n^{o(\log n)}$ cannot beat random guessing for such CSP Chan et al. [FOCS 2013, IEEE, Piscataway, NJ, 2013, pp. 350--359]. Our bounds are obtained by exploiting and extending the recent progress in communication complexity for “lifting" query lower bounds to communication problems. The main ingredient in our results is a new structural result on “high-entropy rectangles” that may be of independent interest in communication complexity.

中文翻译：

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通过 Juntas 和弱指数下界逼近 CSP 的 LP 松弛的矩形

SIAM 计算杂志，超前印刷。
我们表明，对于约束满足问题 (CSP)，弱指数大小的线性规划松弛与由 $n^{\Omega(1)}$-rounds of Sherali--Adams 线性规划层次结构描述的显式线性规划一样强大。结合 Sherali--Adams 层次结构的已知下限，我们获得了线性规划松弛的次指数大小下限，这些下限击败了许多 CSP（如 MAX-CUT 和 MAX-3SAT）的随机猜测。与之前的结果相比，这几乎是指数级的改进；以前，只知道大小为 $n^{o(\log n)}$ 的线性程序无法击败 CSP Chan 等人的随机猜测。[FOCS 2013, IEEE, Piscataway, NJ, 2013, pp. 350--359]。我们的边界是通过利用和扩展最近在“提升”通信复杂性方面的进展而获得的 查询通信问题的下限。我们结果的主要成分是“高熵矩形”的新结构结果，它可能对通信复杂性具有独立的兴趣。