{"paper":{"title":"A Composition Theorem via Conflict Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Swagato Sanyal","submitted_at":"2018-01-10T09:57:14Z","abstract_excerpt":"Let $\\R(\\cdot)$ stand for the bounded-error randomized query complexity. We show that for any relation $f \\subseteq \\{0,1\\}^n \\times \\mathcal{S}$ and partial Boolean function $g \\subseteq \\{0,1\\}^n \\times \\{0,1\\}$, $\\R_{1/3}(f \\circ g^n) = \\Omega(\\R_{4/9}(f) \\cdot \\sqrt{\\R_{1/3}(g)})$. Independently of us, Gavinsky, Lee and Santha \\cite{newcomp} proved this result. By an example demonstrated in their work, this bound is optimal. We prove our result by introducing a novel complexity measure called the \\emph{conflict complexity} of a partial Boolean function $g$, denoted by $\\chi(g)$, which may "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03285","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"}