{"paper":{"title":"Sign-Rank Can Increase Under Intersection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Justin Thaler, Mark Bun, Nikhil S. Mande","submitted_at":"2019-03-01T21:29:13Z","abstract_excerpt":"The communication class $\\mathbf{UPP}^{\\text{cc}}$ is a communication analog of the Turing Machine complexity class $\\mathbf{PP}$. It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension complexity), and is essentially the most powerful communication class against which we know how to prove lower bounds.\n  For a communication problem $f$, let $f \\wedge f$ denote the function that evaluates $f$ on two disjoint inputs and outputs the AND of the results. We exhibit a communication problem $f$ with $\\mathbf{UPP}(f)= O(\\log n)$, and $\\mathbf{UPP}(f \\wedge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00544","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"}