{"paper":{"title":"Short $\\mathsf{Res}^*(\\mathsf{polylog})$ refutations if and only if narrow $\\mathsf{Res}$ refutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.CC","authors_text":"Massimo Lauria","submitted_at":"2013-10-21T20:03:40Z","abstract_excerpt":"In this note we show that any $k$-CNF which can be refuted by a quasi-polynomial $\\mathsf{Res}^*(\\mathsf{polylog})$ refutation has a \"narrow\" refutation in $\\mathsf{Res}$ (i.e., of poly-logarithmic width). We also show the converse implication: a narrow Resolution refutation can be simulated by a short $\\mathsf{Res}^*(\\mathsf{polylog})$ refutation.\n  The author does not claim priority on this result. The technical part of this note bears similarity with the relation between $d$-depth Frege refutations and tree-like $d+1$-depth Frege refutations outlined in (Kraj\\'i\\v{c}ek 1994, Journal of Symb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5714","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"}