Asymptotics of the number of 2-threshold functions

Abstract

A $k$-threshold function on a rectangular grid of size $m\times n$ is the conjunction of $k$ threshold functions on the same domain. In this paper, we focus on the case $k=2$ and show that the number of two-dimensional 2-threshold functions is~$\frac{25}{12{\pi }^4}{m}^4{n}^4+o(m^4{n}^4)$.

26 pages