{"paper":{"title":"Tight Bounds for the Distribution-Free Testing of Monotone Conjunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Jinyu Xie, Xi Chen","submitted_at":"2015-11-10T23:09:47Z","abstract_excerpt":"We improve both upper and lower bounds for the distribution-free testing of monotone conjunctions.\n  Given oracle access to an unknown Boolean function $f:\\{0,1\\}^n \\rightarrow \\{0,1\\}$ and sampling oracle access to an unknown distribution $\\mathcal{D}$ over $\\{0,1\\}^n$, we present an $\\tilde{O}(n^{1/3}/\\epsilon^5)$-query algorithm that tests whether $f$ is a monotone conjunction versus $\\epsilon$-far from any monotone conjunction with respect to $\\mathcal{D}$. This improves the previous best upper bound of $\\tilde{O}(n^{1/2}/\\epsilon)$ by Dolev and Ron when $1/\\epsilon$ is small compared to $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03333","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"}