ON THE MINIMAL TEACHING SETS OF TWO-DIMENSIONAL THRESHOLD FUNCTIONS.
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| Title: | ON THE MINIMAL TEACHING SETS OF TWO-DIMENSIONAL THRESHOLD FUNCTIONS. |
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| Authors: | ALEKSEYEV, MAX A.1 maxal@gwu.edu, BASOVA, MARINA G.2 mbas@inbox.ru, ZOLOTYKH, NIKOLAI YU.3 olotykh@vmk.unn.ru |
| Source: | SIAM Journal on Discrete Mathematics. 2015, Vol. 29 Issue 1, p157-165. 9p. |
| Subjects: | Function point analysis, Functional analysis, Functional differential equations, Calculus of variations, Functional equations |
| Abstract: | It is known that a minimal teaching set of any threshold function on the two-dimensional rectangular grid consists of 3 or 4 points. We derive exact formulae for the numbers of functions corresponding to these values and further refine them in the case of a minimal teaching set of size 3. We also prove that the average cardinality of the minimal teaching sets of threshold functions is asymptotically 7/2. We further present corollaries of these results concerning some special arrangements of lines in the plane. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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