{"paper":{"title":"Witness of unsatisfiability for a random 3-satisfiability formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cs.CC","authors_text":"Erik Aurell, Hai-Jun Zhou, Lu-Lu Wu, Mikko Alava, Pekka Orponen","submitted_at":"2013-03-11T02:47:07Z","abstract_excerpt":"The random 3-satisfiability (3-SAT) problem is in the unsatisfiable (UNSAT) phase when the clause density $\\alpha$ exceeds a critical value $\\alpha_s \\approx 4.267$. However, rigorously proving the unsatisfiability of a given large 3-SAT instance is extremely difficult. In this paper we apply the mean-field theory of statistical physics to the unsatisfiability problem, and show that a specific type of UNSAT witnesses (Feige-Kim-Ofek witnesses) can in principle be constructed when the clause density $\\alpha > 19$. We then construct Feige-Kim-Ofek witnesses for single 3-SAT instances through a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2413","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"}