{"paper":{"title":"A Composition Theorem for Randomized Query Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anurag Anshu, Dmitry Gavinsky, Miklos Santha, Priyanka Mukhopadhyay, Rahul Jain, Srijita Kundu, Swagato Sanyal, Troy Lee","submitted_at":"2017-06-01T15:09:27Z","abstract_excerpt":"Let the randomized query complexity of a relation for error probability $\\epsilon$ be denoted by $R_\\epsilon(\\cdot)$. We prove that for any relation $f \\subseteq \\{0,1\\}^n \\times \\mathcal{R}$ and Boolean function $g:\\{0,1\\}^m \\rightarrow \\{0,1\\}$, $R_{1/3}(f\\circ g^n) = \\Omega(R_{4/9}(f)\\cdot R_{1/2-1/n^4}(g))$, where $f \\circ g^n$ is the relation obtained by composing $f$ and $g$. We also show that $R_{1/3}\\left(f \\circ \\left(g^\\oplus_{O(\\log n)}\\right)^n\\right)=\\Omega(\\log n \\cdot R_{4/9}(f) \\cdot R_{1/3}(g))$, where $g^\\oplus_{O(\\log n)}$ is the function obtained by composing the xor functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00335","kind":"arxiv","version":2},"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"}