{"paper":{"title":"Computing Majority by Constant Depth Majority Circuits with Low Fan-in Gates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Alexander S. Kulikov, Vladimir V. Podolskii","submitted_at":"2016-10-09T15:37:17Z","abstract_excerpt":"We study the following computational problem: for which values of $k$, the majority of $n$ bits $\\text{MAJ}_n$ can be computed with a depth two formula whose each gate computes a majority function of at most $k$ bits? The corresponding computational model is denoted by $\\text{MAJ}_k \\circ \\text{MAJ}_k$. We observe that the minimum value of $k$ for which there exists a $\\text{MAJ}_k \\circ \\text{MAJ}_k$ circuit that has high correlation with the majority of $n$ bits is equal to $\\Theta(n^{1/2})$. We then show that for a randomized $\\text{MAJ}_k \\circ \\text{MAJ}_k$ circuit computing the majority "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02686","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"}