{"paper":{"title":"A Strong XOR Lemma for Randomized Query Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Hariharan Srinivasulu, Jae Tak Kim, Joshua Brody, Peem Lerdputtipongporn","submitted_at":"2020-07-10T19:29:52Z","abstract_excerpt":"We give a strong direct sum theorem for computing $xor \\circ g$. Specifically, we show that for every function g and every $k\\geq 2$, the randomized query complexity of computing the xor of k instances of g satisfies $\\overline{R}_\\eps(xor\\circ g) = \\Theta(k \\overline{R}_{\\eps/k}(g))$. This matches the naive success amplification upper bound and answers a conjecture of Blais and Brody (CCC19).\n  As a consequence of our strong direct sum theorem, we give a total function g for which $R(xor \\circ g) = \\Theta(k \\log(k)\\cdot R(g))$, answering an open question from Ben-David et al.(arxiv:2006.10957"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.05580","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.05580/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}