{"paper":{"title":"Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LO"],"primary_cat":"cs.CC","authors_text":"Enrico Malizia, Georg Gottlob","submitted_at":"2014-07-10T19:28:11Z","abstract_excerpt":"The hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs $\\mathcal{G}$ and $\\mathcal{H}$, decide whether $\\mathcal{H}$ consists precisely of all minimal transversals of $\\mathcal{G}$ (in which case we say that $\\mathcal{G}$ is the dual of $\\mathcal{H}$). This problem is equivalent to deciding whether two given non-redundant monotone DNFs are dual. It is known that non-DUAL, the complementary problem to DUAL, is in $\\mathrm{GC}(\\log^2 n,\\mathrm{PTIME})$, where $\\mathrm{GC}(f(n),\\mathcal{C})$ denotes the complexity class of all problems that after a nondeterministi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2912","kind":"arxiv","version":4},"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"}