{"paper":{"title":"Beyond Talagrand Functions: New Lower Bounds for Testing Monotonicity and Unateness","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":"2017-02-22T20:38:35Z","abstract_excerpt":"We prove a lower bound of $\\tilde{\\Omega}(n^{1/3})$ for the query complexity of any two-sided and adaptive algorithm that tests whether an unknown Boolean function $f:\\{0,1\\}^n\\rightarrow \\{0,1\\}$ is monotone or far from monotone. This improves the recent bound of $\\tilde{\\Omega}(n^{1/4})$ for the same problem by Belovs and Blais [BB15]. Our result builds on a new family of random Boolean functions that can be viewed as a two-level extension of Talagrand's random DNFs.\n  Beyond monotonicity, we also prove a lower bound of $\\tilde{\\Omega}(n^{2/3})$ for any two-sided and adaptive algorithm, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06997","kind":"arxiv","version":2},"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"}