{"paper":{"title":"A Characterization of Approximation Resistance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Madhur Tulsiani, Pratik Worah, Subhash Khot","submitted_at":"2013-05-23T17:52:58Z","abstract_excerpt":"A predicate f:{-1,1}^k -> {0,1} with \\rho(f) = \\frac{|f^{-1}(1)|}{2^k} is called {\\it approximation resistant} if given a near-satisfiable instance of CSP(f), it is computationally hard to find an assignment that satisfies at least \\rho(f)+\\Omega(1) fraction of the constraints.\n  We present a complete characterization of approximation resistant predicates under the Unique Games Conjecture. We also present characterizations in the {\\it mixed} linear and semi-definite programming hierarchy and the Sherali-Adams linear programming hierarchy. In the former case, the characterization coincides with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5500","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}