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On the number of two-dimensional threshold functions

Max A. Alekseyev
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Abstract

A two-dimensional threshold function of k-valued logic can be viewed as coloring of the points of a k x k square lattice into two colors such that there exists a straight line separating points of different colors. For the number of such functions only asymptotic bounds are known. We give an exact formula for the number of two-dimensional threshold functions and derive more accurate asymptotics.

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Max A. Alekseyev. 2010-10-01. On the number of two-dimensional threshold functions. https://doi.org/10.1137/090750184

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