EN|RU Volume 19, No 5, 2012, P. 35-46 UDC 519.7 N. Yu. Zolotykh, A. Yu. Chirkov  În an upper bound for the cardinality of a minimal teaching set of a threshold function Abstract: 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. Keywords: threshold function, teaching set, separation property. Zolotykh Nikolai Yurievich 1 Chirkov Alexander Yurievich 1 1. Nizhniy Novgorod State University, 23 Gagarina ave., 603950 Nizhniy Novgorod, Russia e-mail: zolotykh@vmk.unn.ru, chirkov@vmk.unn.ru © Sobolev Institute of Mathematics, 2015