文章基本信息

标题：Lower Bounds for Multiplication via Network Coding
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作者：Peyman Afshani ; Casper Benjamin Freksen ; Lior Kamma 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：132
页码：1-12
DOI：10.4230/LIPIcs.ICALP.2019.10
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Circuit Complexity; Circuit Lower Bounds; Multiplication; Network Coding; Fine-Grained Complexity