{"paper":{"title":"A near-optimal direct-sum theorem for communication complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Rahul Jain","submitted_at":"2020-08-17T10:04:08Z","abstract_excerpt":"We show a near optimal direct-sum theorem for the two-party randomized communication complexity. Let $f\\subseteq X \\times Y\\times Z$ be a relation, $\\varepsilon> 0$ and $k$ be an integer. We show, $$\\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(f^k) \\cdot \\log(\\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(f^k)) \\ge \\Omega(k \\cdot \\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(f)) \\enspace,$$ where $f^k= f \\times \\ldots \\times f$ ($k$-times) and $\\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(\\cdot)$ represents the public-coin randomized communication complexity with worst-case error $\\varepsilon$. Given a protocol $\\mathcal{P}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.07188","kind":"arxiv","version":3},"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/2008.07188/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"}