{"paper":{"title":"Parity Decision Tree Complexity and 4-Party Communication Complexity of XOR-functions Are Polynomially Equivalent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Penghui Yao","submitted_at":"2015-06-09T14:42:20Z","abstract_excerpt":"In this note, we study the relation between the parity decision tree complexity of a boolean function $f$, denoted by $\\mathrm{D}_{\\oplus}(f)$, and the $k$-party number-in-hand multiparty communication complexity of the XOR functions $F(x_1,\\ldots, x_k)= f(x_1\\oplus\\cdots\\oplus x_k)$, denoted by $\\mathrm{CC}^{(k)}(F)$. It is known that $\\mathrm{CC}^{(k)}(F)\\leq k\\cdot\\mathrm{D}_{\\oplus}(f)$ because the players can simulate the parity decision tree that computes $f$. In this note, we show that \\[\\mathrm{D}_{\\oplus}(f)\\leq O\\big(\\mathrm{CC}^{(4)}(F)^5\\big).\\] Our main tool is a recent result fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02936","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":""},"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"}