On number of two-dimensional threshold functions
نویسنده
چکیده
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 asymptotics that improves previously known.
منابع مشابه
Note on the Number of Two-Dimensional Threshold Functions
A two-dimensional threshold function of k-valued logic can be viewed as coloring of the points of a k × 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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