کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4950749 | 1440715 | 2016 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On teaching sets of k-threshold functions
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
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چکیده انگلیسی
In this paper we study teaching sets of k-threshold functions, i.e. functions that can be represented as a conjunction of k threshold functions. We reveal a connection between essential points of k threshold functions and essential points of the corresponding k-threshold function. We show that in two-dimensional case the number of minimal teaching sets of a 2-threshold function can grow as Ω(n2). We also consider the class of polytopes with vertices in the d-dimensional cube. Each polytope from this class can be defined by a k-threshold function for some k. We prove that such a polytope has a unique minimal teaching set which is equal to the set of its essential points. For d=2 we describe structure of the minimal teaching set of a polytope and show that its cardinality is either Î(n2) or O(n) and depends on the perimeter and the minimum angle of the polytope.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Information and Computation - Volume 251, December 2016, Pages 301-313
Journal: Information and Computation - Volume 251, December 2016, Pages 301-313
نویسندگان
Elena Zamaraeva,