Asymptotics of the number of 2-threshold functions
نویسندگان
چکیده
A k-threshold function on a rectangular grid of size m×n is the conjunction k threshold functions same domain. In this paper, we focus case k=2 and show that number two-dimensional 2-threshold 2512π4m4n4+o(m4n4).
منابع مشابه
Asymptotics of the number of threshold functions on a two-dimensional rectangular grid
Let m,n ≥ 2, m ≤ n. It is well-known that the number of (twodimensional) threshold functions on an m× n rectangular grid is t(m,n) = 6 π (mn) +O(mn logn) +O(mn log logn) = 6 π (mn) +O(mn logm). We improve the error term by showing that t(m,n) = 6 π (mn) +O(mn).
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On number of two-dimensional threshold functions
2-D threshold function f is a function defined on the integer interior of a rectangular area [0, m] × [0, n] on a plane and takes values from the set {0, 1} such that there is a straight line separating the pre-images f −1 (0) and f −1 (1). For the number of such functions only asymptotic bounds were known. We give an exact formula for the number of 2-D threshold functions and derive an asympto...
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ژورنال
عنوان ژورنال: Information & Computation
سال: 2021
ISSN: ['0890-5401', '1090-2651']
DOI: https://doi.org/10.1016/j.ic.2021.104742