A characterization of 2-threshold functions via pairs of prime segments

07/08/2020

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by   Elena Zamaraeva, et al.

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A {0,1}-valued function on a two-dimensional rectangular grid is called threshold if its sets of zeros and ones are separable by a straight line. In this paper we study 2-threshold functions, i.e. functions representable as the conjunction of two threshold functions. We provide a characterization of 2-threshold functions by pairs of oriented prime segments, where each such segment is defined by an ordered pair of adjacent integer points.