{"paper":{"title":"Resolution and the binary encoding of combinatorial principles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Barnaby Martin, Nicola Galesi, Stefan Dantchev","submitted_at":"2018-09-08T17:41:16Z","abstract_excerpt":"We investigate the size complexity of proofs in $Res(s)$ -- an extension of Resolution working on $s$-DNFs instead of clauses -- for families of contradictions given in the {\\em unusual binary} encoding. A motivation of our work is size lower bounds of refutations in Resolution for families of contradictions in the usual unary encoding. Our main interest is the $k$-Clique Principle, whose Resolution complexity is still unknown.\n  Our main result is a $n^{\\Omega(k)}$ lower bound for the size of refutations of the binary $k$-Clique Principle in $Res(\\lfloor \\frac{1}{2}\\log \\log n\\rfloor)$. This "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02843","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"}