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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","authors_text":"Dmitry Gavinsky, Miklos Santha, Swagato Sanyal, Troy Lee","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2018-11-27T00:11:08Z","title":"A composition theorem for randomized query complexity via max conflict complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10752","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9ca6edadf1b41ad25a16ffff96c97b7ca82a2c3defdb3457f60b20823f7a9cc7","target":"record","created_at":"2026-05-17T23:59:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"66ba8854c06f49d227eda217b0551cd6887fc499b4303489746d019ca777f148","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2018-11-27T00:11:08Z","title_canon_sha256":"51fd171753586825ca971b6830e8a9b8762d1828edfc37277330a897842557aa"},"schema_version":"1.0","source":{"id":"1811.10752","kind":"arxiv","version":1}},"canonical_sha256":"269a50c94dbaab9f4e7adda3037b06e0b6093c62a735b18d841d080c65c141de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"269a50c94dbaab9f4e7adda3037b06e0b6093c62a735b18d841d080c65c141de","first_computed_at":"2026-05-17T23:59:47.635980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:47.635980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NZn4i3pCU4I4Lqhs4AMcgCI0RtyIxzpiWp6HKIIbW2LsD6mckjDAhBjvznyDLj7dkz/SABm6p8xF/TLHPd0wDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:47.636465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.10752","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ca6edadf1b41ad25a16ffff96c97b7ca82a2c3defdb3457f60b20823f7a9cc7","sha256:367d6b84a6b7cb8d2fa508dc219513cbd2b0a9b5cca04538212e52d62157d3f9"],"state_sha256":"75c905becd8df0bc6ff7124735dda8e2bc81fb882fd8e31b9b5ff8c4f9147910"}