{"paper":{"title":"Testing Unateness of Real-Valued Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Meiram Murzabulatov, Ramesh Krishnan S. Pallavoor, Roksana Baleshzar, Sofya Raskhodnikova","submitted_at":"2016-08-27T02:49:18Z","abstract_excerpt":"We give a unateness tester for functions of the form $f:[n]^d\\rightarrow R$, where $n,d\\in \\mathbb{N}$ and $R\\subseteq \\mathbb{R}$ with query complexity $O(\\frac{d\\log (\\max(d,n))}{\\epsilon})$. Previously known unateness testers work only for Boolean functions over the domain $\\{0,1\\}^d$. We show that every unateness tester for real-valued functions over hypergrid has query complexity $\\Omega(\\min\\{d, |R|^2\\})$. Consequently, our tester is nearly optimal for real-valued functions over $\\{0,1\\}^d$. We also prove that every nonadaptive, 1-sided error unateness tester for Boolean functions needs "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07652","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"}