{"paper":{"title":"Sum of squares lower bounds for refuting any CSP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"David Witmer, Pravesh K. Kothari, Ryan O'Donnell, Ryuhei Mori","submitted_at":"2017-01-17T03:36:34Z","abstract_excerpt":"Let $P:\\{0,1\\}^k \\to \\{0,1\\}$ be a nontrivial $k$-ary predicate. Consider a random instance of the constraint satisfaction problem $\\mathrm{CSP}(P)$ on $n$ variables with $\\Delta n$ constraints, each being $P$ applied to $k$ randomly chosen literals. Provided the constraint density satisfies $\\Delta \\gg 1$, such an instance is unsatisfiable with high probability. The \\emph{refutation} problem is to efficiently find a proof of unsatisfiability.\n  We show that whenever the predicate $P$ supports a $t$-\\emph{wise uniform} probability distribution on its satisfying assignments, the sum of squares "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04521","kind":"arxiv","version":1},"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"}