{"paper":{"title":"A o(n) monotonicity tester for Boolean functions over the hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"C. Seshadhri, Deeparnab Chakrabarty","submitted_at":"2013-02-19T08:05:14Z","abstract_excerpt":"A Boolean function $f:\\{0,1\\}^n \\mapsto \\{0,1\\}$ is said to be $\\eps$-far from monotone if $f$ needs to be modified in at least $\\eps$-fraction of the points to make it monotone. We design a randomized tester that is given oracle access to $f$ and an input parameter $\\eps>0$, and has the following guarantee: It outputs {\\sf Yes} if the function is monotonically non-decreasing, and outputs {\\sf No} with probability $>2/3$, if the function is $\\eps$-far from monotone. This non-adaptive, one-sided tester makes $O(n^{7/8}\\eps^{-3/2}\\ln(1/\\eps))$ queries to the oracle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4536","kind":"arxiv","version":3},"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"}