{"paper":{"title":"New algorithms and lower bounds for monotonicity testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Li-Yang Tan, Rocco A. Servedio, Xi Chen","submitted_at":"2014-12-17T22:26:10Z","abstract_excerpt":"We consider the problem of testing whether an unknown Boolean function $f$ is monotone versus $\\epsilon$-far from every monotone function. The two main results of this paper are a new lower bound and a new algorithm for this well-studied problem.\n  Lower bound: We prove an $\\tilde{\\Omega}(n^{1/5})$ lower bound on the query complexity of any non-adaptive two-sided error algorithm for testing whether an unknown Boolean function $f$ is monotone versus constant-far from monotone. This gives an exponential improvement on the previous lower bound of $\\Omega(\\log n)$ due to Fischer et al. [FLN+02]. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5655","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"}