{"paper":{"title":"Boolean function monotonicity testing requires (almost) $n^{1/2}$ non-adaptive queries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anindya De, Li-Yang Tan, Rocco A. Servedio, Xi Chen","submitted_at":"2014-12-17T22:37:54Z","abstract_excerpt":"We prove a lower bound of $\\Omega(n^{1/2 - c})$, for all $c>0$, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an $n$-variable Boolean function is monotone versus constant-far from monotone. This improves a $\\tilde{\\Omega}(n^{1/5})$ lower bound for the same problem that was recently given in [CST14] and is very close to $\\Omega(n^{1/2})$, which we conjecture is the optimal lower bound for this model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5657","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"}