{"paper":{"title":"An $O(n^{0.4732})$ upper bound on the complexity of the GKS communication game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Mario Szegedy","submitted_at":"2015-06-22T03:57:07Z","abstract_excerpt":"We give an $5\\cdot n^{\\log_{30}5}$ upper bund on the complexity of the communication game introduced by G. Gilmer, M. Kouck\\'y and M. Saks \\cite{saks} to study the Sensitivity Conjecture \\cite{linial}, improving on their $\\sqrt{999\\over 1000}\\sqrt{n}$ bound. We also determine the exact complexity of the game up to $n\\le 9$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06456","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":""},"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"}