{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:22Z","timestamp":1753894402487,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We study the extent to which it is possible to approximate the optimal value\nof a Unique Games instance in Fixed-Point Logic with Counting (FPC). Formally,\nwe prove lower bounds against the accuracy of FPC-interpretations that map\nUnique Games instances (encoded as relational structures) to rational numbers\ngiving the approximate fraction of constraints that can be satisfied. We prove\ntwo new FPC-inexpressibility results for Unique Games: the existence of a\n$(1\/2, 1\/3 + \\delta)$-inapproximability gap, and inapproximability to within\nany constant factor. Previous recent work has established similar\nFPC-inapproximability results for a small handful of other problems. Our\nconstruction builds upon some of these ideas, but contains a novel technique.\nWhile most FPC-inexpressibility results are based on variants of the\nCFI-construction, ours is significantly different. We start with a graph of\nvery large girth and label the edges with random affine vector spaces over\n$\\mathbb{F}_2$ that determine the constraints in the two structures.\nDuplicator's strategy involves maintaining a partial isomorphism over a minimal\ntree that spans the pebbled vertices of the graph.<\/jats:p>","DOI":"10.46298\/lmcs-20(2:3)2024","type":"journal-article","created":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T15:25:24Z","timestamp":1713281124000},"source":"Crossref","is-referenced-by-count":0,"title":["Inapproximability of Unique Games in Fixed-Point Logic with Counting"],"prefix":"10.46298","volume":"Volume 20, Issue 2","author":[{"given":"Jamie","family":"Tucker-Foltz","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,4,10]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/13380\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/13380\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T15:25:24Z","timestamp":1713281124000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/9090"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,10]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(2:3)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2104.04566v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2104.04566v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2104.04566","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2104.04566","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,4,10]]},"article-number":"9090"}}