{"paper":{"title":"Boolean Unateness Testing with $\\widetilde{O}(n^{3/4})$ Adaptive Queries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Erik Waingarten, Jinyu Xie, Xi Chen","submitted_at":"2017-08-19T00:20:44Z","abstract_excerpt":"We give an adaptive algorithm which tests whether an unknown Boolean function $f\\colon \\{0, 1\\}^n \\to\\{0, 1\\}$ is unate, i.e. every variable of $f$ is either non-decreasing or non-increasing, or $\\epsilon$-far from unate with one-sided error using $\\widetilde{O}(n^{3/4}/\\epsilon^2)$ queries. This improves on the best adaptive $O(n/\\epsilon)$-query algorithm from Baleshzar, Chakrabarty, Pallavoor, Raskhodnikova and Seshadhri when $1/\\epsilon \\ll n^{1/4}$. Combined with the $\\widetilde{\\Omega}(n)$-query lower bound for non-adaptive algorithms with one-sided error of [CWX17, BCPRS17], we conclude"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05786","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"}