{"paper":{"title":"On Block Sensitivity and Fractional Block Sensitivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Andris Ambainis, Jevg\\=enijs Vihrovs, Kri\\v{s}j\\=anis Pr\\=usis","submitted_at":"2018-10-04T18:51:04Z","abstract_excerpt":"We investigate the relation between the block sensitivity $\\text{bs}(f)$ and fractional block sensitivity $\\text{fbs}(f)$ complexity measures of Boolean functions. While it is known that $\\text{fbs}(f) = O(\\text{bs}(f)^2)$, the best known separation achieves $\\text{fbs}(f) = \\left(\\frac{1}{3\\sqrt2} +o(1)\\right) \\text{bs(f)}^{3/2}$. We improve the constant factor and show a family of functions that give $\\text{fbs}(f) = \\left(\\frac{1}{\\sqrt6}-o(1)\\right) \\text{bs}(f)^{3/2}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02393","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"}