{"paper":{"title":"Strong XOR Lemma for Information Complexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.CC","authors_text":"Huacheng Yu, Pachara Sawettamalya","submitted_at":"2024-11-20T03:36:48Z","abstract_excerpt":"For any $\\{0,1\\}$-valued function $f$, its \\emph{$n$-folded XOR} is the function $f^{\\oplus n}$ where $f^{\\oplus n}(X_1, \\ldots, X_n) = f(X_1) \\oplus \\cdots \\oplus f(X_n)$. Given a procedure for computing the function $f$, one can apply a ``naive\" approach to compute $f^{\\oplus n}$ by computing each $f(X_i)$ independently, followed by XORing the outputs. This approach uses $n$ times the resources required for computing $f$.\n  In this paper, we prove a strong XOR lemma for \\emph{information complexity} in the two-player randomized communication model: if computing $f$ with an error probability "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13015","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/2411.13015/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"}