{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T23:23:00Z","timestamp":1783984980071,"version":"3.55.0"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2026,2,22]]},"abstract":"<jats:p>We propose a framework of algorithm vs. hardness for all Max-CSPs and demonstrate it for a large class of predicates. This framework extends the work of Raghavendra [STOC, 2008], who showed a similar result for almost satisfiable Max-CSPs.   Our framework is based on a new hybrid approximation algorithm, which uses a combination of the Gaussian elimination technique (i.e., solving a system of linear equations over an Abelian group) and the semidefinite programming relaxation. We complement our algorithm with a matching dictator vs. quasirandom test that has perfect completeness.   The analysis of our dictator vs. quasirandom test is based on a novel invariance principle, which we call the mixed invariance principle. Our mixed invariance principle is an extension of the invariance principle of Mossel, O'Donnell and Oleszkiewicz [Annals of Mathematics, 2010] which plays a crucial role in Raghavendra's work. The mixed invariance principle allows one to relate 3-wise correlations over discrete probability spaces with expectations over spaces that are a mixture of Guassian spaces and Abelian groups, and may be of independent interest.<\/jats:p>\n                  <jats:p>89 pages. This is the TheoretiCS journal version<\/jats:p>","DOI":"10.46298\/theoretics.26.9","type":"journal-article","created":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T08:45:12Z","timestamp":1779266712000},"source":"Crossref","is-referenced-by-count":1,"title":["On Approximability of Satisfiable k-CSPs: V"],"prefix":"10.46298","volume":"Volume 5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3878-9241","authenticated-orcid":false,"given":"Amey","family":"Bhangale","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-9246-4011","authenticated-orcid":false,"given":"Subhash","family":"Khot","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8093-1328","authenticated-orcid":false,"given":"Dor","family":"Minzer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"25203","published-online":{"date-parts":[[2026,5,20]]},"container-title":["TheoretiCS"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2408.15377v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2408.15377v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T08:45:12Z","timestamp":1779266712000},"score":1,"resource":{"primary":{"URL":"https:\/\/theoretics.episciences.org\/16123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,20]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/theoretics.26.9","relation":{"has-preprint":[{"id-type":"arxiv","id":"2408.15377v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2408.15377","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2408.15377","asserted-by":"subject"}]},"ISSN":["2751-4838"],"issn-type":[{"value":"2751-4838","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,20]]},"article-number":"16123"}}