{"paper":{"title":"Junta correlation is testable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Anindya De, Elchanan Mossel, Joe Neeman","submitted_at":"2019-04-08T17:38:17Z","abstract_excerpt":"The problem of tolerant junta testing is a natural and challenging problem which asks if the property of a function having some specified correlation with a $k$-Junta is testable. In this paper we give an affirmative answer to this question: We show that given distance parameters $\\frac{1}{2} >c_u>c_{\\ell} \\ge 0$, there is a tester which given oracle access to $f:\\{-1,1\\}^n \\rightarrow \\{-1,1\\}$, with query complexity $ 2^k \\cdot \\mathsf{poly}(k,1/|c_u-c_{\\ell}|)$ and distinguishes between the following cases:\n  $\\mathbf{1.}$ The distance of $f$ from any $k$-junta is at least $c_u$;\n  $\\mathbf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04216","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"}