{"paper":{"title":"A composition theorem for randomized query complexity via max conflict complexity","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Dmitry Gavinsky, Miklos Santha, Swagato Sanyal, Troy Lee","submitted_at":"2018-11-27T00:11:08Z","abstract_excerpt":"Let $R_\\epsilon(\\cdot)$ stand for the bounded-error randomized query complexity with error $\\epsilon > 0$. For any relation $f \\subseteq \\{0,1\\}^n \\times S$ and partial Boolean function $g \\subseteq \\{0,1\\}^m \\times \\{0,1\\}$, we show that $R_{1/3}(f \\circ g^n) \\in \\Omega(R_{4/9}(f) \\cdot \\sqrt{R_{1/3}(g)})$, where $f \\circ g^n \\subseteq (\\{0,1\\}^m)^n \\times S$ is the composition of $f$ and $g$. We give an example of a relation $f$ and partial Boolean function $g$ for which this lower bound is tight.\n  We prove our composition theorem by introducing a new complexity measure, the max conflict co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10752","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"}