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oai:drops-oai.dagstuhl.de:10586 2024-03-06T10:46:12Z ddc:004 open_access

Lower Bounds for Multiplication via Network Coding Afshani, Peyman Freksen, Casper Benjamin Kamma, Lior Larsen, Kasper Green Circuit Complexity Circuit Lower Bounds Multiplication Network Coding Fine-Grained Complexity Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, very recently proved by Harvey and van der Hoeven (2019), shows that two n-bit numbers can be multiplied via a boolean circuit of size O(n lg n). 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 revisit classic conjectures in circuit complexity, due to Valiant, and show that the network coding conjecture also implies one of Valiant’s conjectures. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Peyman Afshani and Casper Benjamin Freksen and Lior Kamma and Kasper Green Larsen 2019 Is Part Of LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2019.10 urn:nbn:de:0030-drops-105861 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.10 eng https://creativecommons.org/licenses/by/3.0/legalcode