arXiv:1902.10935cs.DS
Lower Bounds for Multiplication via Network Coding
Abstract
Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, by Fürer, 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 $Ω(n \lg n)$, 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.
According to the article, it rests on a plausible conjecture. I need to read further. [edit] According to the abstract of the paper referred to in the article (https://arxiv.org/abs/1902.10935) it rests on a "central conjecture in the area of network coding". Make of that what…
ogogmadView on HNParent context
There is a (conditional) proof that nlogn is optimal: https://arxiv.org/abs/1902.10935
EvgeniyZhView on HNParent context