{"paper":{"title":"Adaptivity is exponentially powerful for testing monotonicity of halfspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Erik Waingarten, Li-Yang Tan, Rocco A. Servedio, Xi Chen","submitted_at":"2017-06-17T16:11:30Z","abstract_excerpt":"We give a $\\mathrm{poly}(\\log n, 1/\\epsilon)$-query adaptive algorithm for testing whether an unknown Boolean function $f: \\{-1,1\\}^n \\to \\{-1,1\\}$, which is promised to be a halfspace, is monotone versus $\\epsilon$-far from monotone. Since non-adaptive algorithms are known to require almost $\\Omega(n^{1/2})$ queries to test whether an unknown halfspace is monotone versus far from monotone, this shows that adaptivity enables an exponential improvement in the query complexity of monotonicity testing for halfspaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05556","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"}