On an upper bound for the cardinality of a minimal teaching set of a threshold function

A new necessary and sufficient condition for belonging a point to a minimal teaching set of a threshold function of $k$-valued logic is proposed. This allows to extract a large subclass of threshold functions for which the cardinality of the minimal teaching set is bounded from above by a polynomial in $\log_k$ of degree $n-2$ when the number $n$ of variables is fixed. Ill. 1, bibliogr. 17.