Article collection "Mathematical Problems of Cybernetics" №17, Moscow, 2008

Authors:Zolotykh N.Yu.

Bounds for the cardinality of teaching set of a threshold function of many-valued logic

Abstract:

A function f mapping E_{k}^{n}={0,1,…,k-1}^{n} into {0,1} is called threshold if there is a hyperplane separating the points where f(x) = 0 from the points where f(x)=1. A set T⊆ E_{k}^{n} is called teaching for the threshold function f if the values of f in T are enough to restore f in all other points of E_{k}^{n}. The refinements of upper and lower bounds for the cardinality of minimal teaching set for a threshold function are given.