Inapproximability of Unique Games in Fixed-Point Logic with Counting

Jamie Tucker-Foltz
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引用次数: 1

Abstract

We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). We prove two new FPC- inexpressibility results for Unique Games: the existence of a $\left( {\frac{1}{2},\frac{1}{3} + \delta } \right)$-inapproximability gap, and inapproximability to within any constant factor. Previous recent work has established similar FPC-inapproximability results for a small handful of other problems. Our construction builds upon some of these ideas, but contains a novel technique. While most FPC-inexpressibility results are based on variants of the CFI-construction, ours is significantly different.
计数不动点逻辑中唯一对策的不可逼近性
我们研究了在定点计数逻辑(FPC)中近似唯一游戏实例的最优值的可能程度。我们证明了独特游戏的两个新的FPC不可表达性结果:$\left( {\frac{1}{2},\frac{1}{3} + \delta } \right)$ -不可接近性差距的存在,以及在任何常数因子内的不可接近性。以前最近的工作已经在少数其他问题上建立了类似的fpc不可近似性结果。我们的构建基于其中的一些想法,但包含了一种新颖的技术。虽然大多数fpc不可表达性结果是基于cfi结构的变体,但我们的结果却有显著不同。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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