Asymptotics of the number of 2-threshold functions

Elena Zamaraeva, Jovisa Zunic

Published 2020-07-08Version 1

A $k$-threshold function over a two-dimensional rectangular grid $\mathcal{G}_{m,n} = \{0,\dots,m-1\} \times \{0,\dots,n-1\}$ is the conjunction of $k$ linear threshold functions over the same domain. In this paper we focus on the case $k=2$ and show that the number of 2-threshold functions defined on $\mathcal{G}_{m,n}$ is $\dfrac{25}{12\pi^4} m^4 n^4 + o(m^4n^4)$.