{"paper":{"title":"Alternation, Sparsity and Sensitivity : Bounds and Exponential Gaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CC","authors_text":"Jayalal Sarma, Krishnamoorthy Dinesh","submitted_at":"2017-12-15T16:27:26Z","abstract_excerpt":"$\\newcommand{\\sp}{\\mathsf{sparsity}}\\newcommand{\\s}{\\mathsf{s}}\\newcommand{\\al}{\\mathsf{alt}}$ The well-known Sensitivity Conjecture states that for any Boolean function $f$, block sensitivity of $f$ is at most polynomial in sensitivity of $f$ (denoted by $\\s(f)$). The XOR Log-Rank Conjecture states that for any $n$ bit Boolean function, $f$ the communication complexity of a related function $f^{\\oplus}$ on $2n$ bits, (defined as $f^{\\oplus}(x,y)=f(x\\oplus y)$) is at most polynomial in logarithm of the sparsity of $f$ (denoted by $\\sp(f)$). A recent result of Lin and Zhang (2017) implies that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05735","kind":"arxiv","version":2},"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"}