{"paper":{"title":"Phase Transition in Matched Formulas and a Heuristic for Biclique Satisfiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Department of Theoretical Computer Science, Faculty of Mathematics, Mathematical Logic), Milo\\v{s} Chrom\\'y (1), Petr Ku\\v{c}era (1) ((1) Charles University, Physics","submitted_at":"2018-08-06T08:37:44Z","abstract_excerpt":"A matched formula is a CNF formula whose incidence graph admits a matching which matches a distinct variable to every clause. We study phase transition in a context of matched formulas and their generalization of biclique satisfiable formulas. We have performed experiments to find a phase transition of property \"being matched\" with respect to the ratio $m/n$ where $m$ is the number of clauses and $n$ is the number of variables of the input formula $\\varphi$. We compare the results of experiments to a theoretical lower bound which was shown by Franco and Gelder (2003). Any matched formula is sa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01774","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"}