{"paper":{"title":"A note on the partition bound for one-way classical communication complexity","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Jo\\~ao F. Doriguello, Rahul Jain, Srinivasan Arunachalam","submitted_at":"2023-02-21T04:04:38Z","abstract_excerpt":"We present a linear program for the one-way version of the partition bound (denoted $\\mathsf{prt}^1_\\varepsilon(f)$). We show that it characterizes one-way randomized communication complexity $\\mathsf{R}_\\varepsilon^1(f)$ with shared randomness of every partial function $f:\\mathcal{X}\\times\\mathcal{Y}\\to\\mathcal{Z}$, i.e., for $\\delta,\\varepsilon\\in(0,1/2)$, $\\mathsf{R}_\\varepsilon^1(f) \\geq \\log\\mathsf{prt}_\\varepsilon^1(f)$ and $\\mathsf{R}_{\\varepsilon+\\delta}^1(f) \\leq \\log\\mathsf{prt}_\\varepsilon^1(f) + \\log\\log(1/\\delta)$. This improves upon the characterization of $\\mathsf{R}_\\varepsilon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.10431","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.10431/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"}