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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 $(1.007) \\cdot 2.64944^h$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.7565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-09-29T10:00:34Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"e3ff5d8da5bd85207c42935a0ef68e08e99b809714484b3fa90db64c3e78e132","abstract_canon_sha256":"a9611fae1daf9742b11fa6f3f48ee0701e2bbd049b0e5f9c47da71690c455a01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:56.554781Z","signature_b64":"maQSgl5j1DzycFPUT4xuRDWiM71sg0oF4lqtGyG1J1yyYAwrTQfEDkjimKc9J6Yi+pgtnlAQgIh8cdIZ/iCCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b83da441fc810d86a0bd0995bbcb05c42e05f0daa2bf8a1cf34599c11438c26","last_reissued_at":"2026-05-18T03:11:56.553917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:56.553917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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