no code implementations • 19 Feb 2021 • Alexander S. Kulikov, Danila Pechenev, Nikita Slezkin
One of the reasons of this behavior is that the search space is enormous: the number of circuits of size $s$ is $s^{\Theta(s)}$, the number of Boolean functions on $n$ variables is $2^{2^n}$.
1 code implementation • 31 Dec 2018 • Alexander S. Kulikov, Ivan Mikhailin, Andrey Mokhov, Vladimir Podolskii
As a simple application of the presented linear-size construction, we show how to multiply two $n\times n$ matrices over an arbitrary semiring in $O(n^2)$ time if one of these matrices is a 0/1-matrix with $O(n)$ zeroes (i. e., a complement of a sparse matrix).
Computational Complexity
