eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-07-04
10:1
10:12
10.4230/LIPIcs.ICALP.2019.10
article
Lower Bounds for Multiplication via Network Coding
Afshani, Peyman
1
Freksen, Casper Benjamin
1
Kamma, Lior
1
Larsen, Kasper Green
1
Computer Science Department, Aarhus University, Denmark
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol132-icalp2019/LIPIcs.ICALP.2019.10/LIPIcs.ICALP.2019.10.pdf
Circuit Complexity
Circuit Lower Bounds
Multiplication
Network Coding
Fine-Grained Complexity