{"paper":{"title":"Lower Bounds for Multiplication via Network Coding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Casper Benjamin Freksen, Kasper Green Larsen, Lior Kamma, Peyman Afshani","submitted_at":"2019-02-28T07:35:19Z","abstract_excerpt":"Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, by F\\\"{u}rer, shows that two $n$-bit numbers can be multiplied via a boolean circuit of size $O(n \\lg n \\cdot 4^{\\lg^*n})$, where $\\lg^*n$ is the very slowly growing iterated logarithm. In this work, we prove that if a central conjecture in the area of network coding is true, then any constant degree boolean circuit for multiplication must have size $\\Omega(n \\lg n)$, thus almost completely settling the complexity of multiplication circuits. We additionally"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10935","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"}