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

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Elena Zamaraeva, Jovisa D. Zunic

Published: 01 Jan 2022, Last Modified: 09 May 2025Theor. Comput. Sci. 2022EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: 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.