{"paper":{"title":"On the Complexity of Random Satisfiability Problems with Planted Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS","math.CO","math.PR"],"primary_cat":"cs.CC","authors_text":"Santosh Vempala, Vitaly Feldman, Will Perkins","submitted_at":"2013-11-19T18:13:32Z","abstract_excerpt":"The problem of identifying a planted assignment given a random $k$-SAT formula consistent with the assignment exhibits a large algorithmic gap: while the planted solution becomes unique and can be identified given a formula with $O(n\\log n)$ clauses, there are distributions over clauses for which the best known efficient algorithms require $n^{k/2}$ clauses. We propose and study a unified model for planted $k$-SAT, which captures well-known special cases. An instance is described by a planted assignment $\\sigma$ and a distribution on clauses with $k$ literals. We define its distribution comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4821","kind":"arxiv","version":8},"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"}