A function f mapping E_kⁿ={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_kⁿ 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_kⁿ. The refinements of upper and lower bounds for the cardinality of minimal teaching set for a threshold function are given.

threshold function, teaching set, deciphering

Mathematical problems and theory of numerical methods