{"paper":{"title":"Communication Complexity of Permutation-Invariant Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.CC","authors_text":"Badih Ghazi, Madhu Sudan, Pritish Kamath","submitted_at":"2015-05-31T19:13:58Z","abstract_excerpt":"Motivated by the quest for a broader understanding of communication complexity of simple functions, we introduce the class of \"permutation-invariant\" functions. A partial function $f:\\{0,1\\}^n \\times \\{0,1\\}^n\\to \\{0,1,?\\}$ is permutation-invariant if for every bijection $\\pi:\\{1,\\ldots,n\\} \\to \\{1,\\ldots,n\\}$ and every $\\mathbf{x}, \\mathbf{y} \\in \\{0,1\\}^n$, it is the case that $f(\\mathbf{x}, \\mathbf{y}) = f(\\mathbf{x}^{\\pi}, \\mathbf{y}^{\\pi})$. Most of the commonly studied functions in communication complexity are permutation-invariant. For such functions, we present a simple complexity meas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00273","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"}