{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VXBVOYOJG4PDGMEFHA5HLDAOUH","short_pith_number":"pith:VXBVOYOJ","schema_version":"1.0","canonical_sha256":"adc35761c9371e333085383a758c0ea1ecd52def7df9bfa8389b66a2315938eb","source":{"kind":"arxiv","id":"1711.10176","version":1},"attestation_state":"computed","paper":{"title":"Computing majority with low-fan-in majority queries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Gleb Posobin","submitted_at":"2017-11-28T08:38:54Z","abstract_excerpt":"In this paper we examine the problem of computing majority function $\\mathrm{MAJ}_n$ on $n$ bits by depth-two formula, where each gate is a majority function on at most $k$ inputs. We present such formula that gives the first nontrivial upper bound for this problem, with $k = \\frac{2}{3} n + 4$. This answers an open question in [Kulikov, Podolskii, 2017].\n  We also look at this problem in adaptive setting - when we are allowed to query for value of $\\mathrm{MAJ}_k$ on any subset, and wish to minimize the number of such queries. We give a simple lower bound for this setting with $\\lceil n/k \\rc"},"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":"1711.10176","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2017-11-28T08:38:54Z","cross_cats_sorted":[],"title_canon_sha256":"be2331aaac4a16cf57fca154ddc86a6cbcec4a8b0f084e4f2cae8022ec604535","abstract_canon_sha256":"c5d1b99cf8709c6bffeabaf1460b61bc42402ff7d154d54f8ea7ad752fc960ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:23.103355Z","signature_b64":"uCa3pg1cNNYAVO5cNI09kNaAZl15pqAqKCiG/xJxAokZExVJzvBMmL658qv+iQYi49uEJnVM0hT+fmiUSg/uDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adc35761c9371e333085383a758c0ea1ecd52def7df9bfa8389b66a2315938eb","last_reissued_at":"2026-05-18T00:29:23.102683Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:23.102683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing majority with low-fan-in majority queries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Gleb Posobin","submitted_at":"2017-11-28T08:38:54Z","abstract_excerpt":"In this paper we examine the problem of computing majority function $\\mathrm{MAJ}_n$ on $n$ bits by depth-two formula, where each gate is a majority function on at most $k$ inputs. We present such formula that gives the first nontrivial upper bound for this problem, with $k = \\frac{2}{3} n + 4$. This answers an open question in [Kulikov, Podolskii, 2017].\n  We also look at this problem in adaptive setting - when we are allowed to query for value of $\\mathrm{MAJ}_k$ on any subset, and wish to minimize the number of such queries. We give a simple lower bound for this setting with $\\lceil n/k \\rc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10176","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1711.10176","created_at":"2026-05-18T00:29:23.102779+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.10176v1","created_at":"2026-05-18T00:29:23.102779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10176","created_at":"2026-05-18T00:29:23.102779+00:00"},{"alias_kind":"pith_short_12","alias_value":"VXBVOYOJG4PD","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VXBVOYOJG4PDGMEF","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VXBVOYOJ","created_at":"2026-05-18T12:31:49.984773+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VXBVOYOJG4PDGMEFHA5HLDAOUH","json":"https://pith.science/pith/VXBVOYOJG4PDGMEFHA5HLDAOUH.json","graph_json":"https://pith.science/api/pith-number/VXBVOYOJG4PDGMEFHA5HLDAOUH/graph.json","events_json":"https://pith.science/api/pith-number/VXBVOYOJG4PDGMEFHA5HLDAOUH/events.json","paper":"https://pith.science/paper/VXBVOYOJ"},"agent_actions":{"view_html":"https://pith.science/pith/VXBVOYOJG4PDGMEFHA5HLDAOUH","download_json":"https://pith.science/pith/VXBVOYOJG4PDGMEFHA5HLDAOUH.json","view_paper":"https://pith.science/paper/VXBVOYOJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.10176&json=true","fetch_graph":"https://pith.science/api/pith-number/VXBVOYOJG4PDGMEFHA5HLDAOUH/graph.json","fetch_events":"https://pith.science/api/pith-number/VXBVOYOJG4PDGMEFHA5HLDAOUH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VXBVOYOJG4PDGMEFHA5HLDAOUH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VXBVOYOJG4PDGMEFHA5HLDAOUH/action/storage_attestation","attest_author":"https://pith.science/pith/VXBVOYOJG4PDGMEFHA5HLDAOUH/action/author_attestation","sign_citation":"https://pith.science/pith/VXBVOYOJG4PDGMEFHA5HLDAOUH/action/citation_signature","submit_replication":"https://pith.science/pith/VXBVOYOJG4PDGMEFHA5HLDAOUH/action/replication_record"}},"created_at":"2026-05-18T00:29:23.102779+00:00","updated_at":"2026-05-18T00:29:23.102779+00:00"}