{"paper":{"title":"Inner Product and Set Disjointness: Beyond Logarithmically Many Parties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Alexander A. Sherstov, Vladimir V. Podolskii","submitted_at":"2017-11-29T03:30:23Z","abstract_excerpt":"A basic goal in complexity theory is to understand the communication complexity of number-on-the-forehead problems $f\\colon(\\{0,1\\}^n)^{k}\\to\\{0,1\\}$ with $k\\gg\\log n$ parties. We study the problems of inner product and set disjointness and determine their randomized communication complexity for every $k\\geq\\log n$, showing in both cases that $\\Theta(1+\\lceil\\log n\\rceil/\\log\\lceil1+k/\\log n\\rceil)$ bits are necessary and sufficient. In particular, these problems admit constant-cost protocols if and only if the number of parties is $k\\geq n^{\\epsilon}$ for some constant $\\epsilon>0.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10661","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"}