{"title":"Inapproximability of Unique Games in Fixed-Point Logic with Counting","authors":"Jamie Tucker-Foltz","doi":"10.1109/LICS52264.2021.9470706","DOIUrl":null,"url":null,"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.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS52264.2021.9470706","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.