Teaching dimension

In computational learning theory, the teaching dimension of a concept class C is defined to be $\max_{c\in C}\{w_C(c)\}$, where ${w_C(c)}$ is the minimum size of a witness set for c in C.

The teaching dimension of a finite concept class can be used to give a lower and an upper bound on the membership query cost of the concept class.

In Stasys Jukna's book "Extremal Combinatorics", a lower bound is given for the teaching dimension:

Let C be a concept class over a finite domain X. If the size of C is greater than

$2^k{|X|\choose k},$

then the teaching dimension of C is greater than k.