{"paper":{"title":"Space proof complexity for random 3-CNFs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"cs.CC","authors_text":"Ilario Bonacina, Mike Molloy, Nicola Galesi, Patrick Bennett, Paul Wollan, Tony Huynh","submitted_at":"2015-03-05T11:46:47Z","abstract_excerpt":"We investigate the space complexity of refuting $3$-CNFs in Resolution and algebraic systems. We prove that every Polynomial Calculus with Resolution refutation of a random $3$-CNF $\\phi$ in $n$ variables requires, with high probability, $\\Omega(n)$ distinct monomials to be kept simultaneously in memory. The same construction also proves that every Resolution refutation $\\phi$ requires, with high probability, $\\Omega(n)$ clauses each of width $\\Omega(n)$ to be kept at the same time in memory. This gives a $\\Omega(n^2)$ lower bound for the total space needed in Resolution to refute $\\phi$. Thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01613","kind":"arxiv","version":3},"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"}