{"paper":{"title":"Biclique coverings, rectifier networks and the cost of $\\varepsilon$-removal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.FL","authors_text":"\\'Ad\\'am D\\'aniel Lelkes, Bal\\'azs Sz\\\"or\\'enyi, Gy\\\"orgy Tur\\'an, Judit Nagy-Gy\\\"orgy, Szabolcs Iv\\'an","submitted_at":"2014-05-30T21:17:39Z","abstract_excerpt":"We relate two complexity notions of bipartite graphs: the minimal weight biclique covering number $\\mathrm{Cov}(G)$ and the minimal rectifier network size $\\mathrm{Rect}(G)$ of a bipartite graph $G$. We show that there exist graphs with $\\mathrm{Cov}(G)\\geq \\mathrm{Rect}(G)^{3/2-\\epsilon}$. As a corollary, we establish that there exist nondeterministic finite automata (NFAs) with $\\varepsilon$-transitions, having $n$ transitions total such that the smallest equivalent $\\varepsilon$-free NFA has $\\Omega(n^{3/2-\\epsilon})$ transitions. We also formulate a version of previous bounds for the weigh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0017","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"}