{"paper":{"title":"Improved bounds for the randomized decision tree complexity of recursive majority","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Ashwin Nayak, David Xiao, Frederic Magniez, Gabor Tardos, Jonah Sherman, Miklos Santha","submitted_at":"2013-09-29T10:00:34Z","abstract_excerpt":"We consider the randomized decision tree complexity of the recursive 3-majority function. We prove a lower bound of $(1/2-\\delta) \\cdot 2.57143^h$ for the two-sided-error randomized decision tree complexity of evaluating height $h$ formulae with error $\\delta \\in [0,1/2)$. This improves the lower bound of $(1-2\\delta)(7/3)^h$ given by Jayram, Kumar, and Sivakumar (STOC'03), and the one of $(1-2\\delta) \\cdot 2.55^h$ given by Leonardos (ICALP'13). Second, we improve the upper bound by giving a new zero-error randomized decision tree algorithm that has complexity at most $(1.007) \\cdot 2.64944^h$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7565","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"}