{"paper":{"title":"Approximating the noise sensitivity of a monotone Boolean function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arsen Vasilyan, Ronitt Rubinfeld","submitted_at":"2019-04-14T19:37:05Z","abstract_excerpt":"The noise sensitivity of a Boolean function $f: \\{0,1\\}^n \\rightarrow \\{0,1\\}$ is one of its fundamental properties. A function of a positive noise parameter $\\delta$, it is denoted as $NS_{\\delta}[f]$. Here we study the algorithmic problem of approximating it for monotone $f$, such that $NS_{\\delta}[f] \\geq 1/n^{C}$ for constant $C$, and where $\\delta$ satisfies $1/n \\leq \\delta \\leq 1/2$. For such $f$ and $\\delta$, we give a randomized algorithm performing $O\\left(\\frac{\\min(1,\\sqrt{n} \\delta \\log^{1.5} n) }{NS_{\\delta}[f]} \\text{poly}\\left(\\frac{1}{\\epsilon}\\right)\\right)$ queries and appro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06745","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"}