Inapproximability of Unique Games in Fixed-Point Logic with Counting

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 g...

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Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 13
Main Author: Tucker-Foltz, Jamie
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Approximation algorithms
Complexity theory
Computer science
Games
Graph theory
Linear algebra
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Summary: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.
DOI:10.1109/LICS52264.2021.9470706