Learnability of languages is a challenging problem
in the domain of formal language identi¯cation. It is
known that the e±ciency of a learning technique can
be measured by the size of some good samples (rep-
resentative or distinctive samples) formally called a
characteristic set. Our research focuses on the char-
acteristic set of k-acceptable languages. We proposed
a Gold-style learning algorithm called KRPNI which
applied the grammatical inference technique to iden-
tify a language and expressed it by a k-DFA. In this
paper, we study the existence of such characteristic
sets. Our theoretical results show that there exists a
polynomial characteristic set for a k-acceptable lan-
guage. It is found that the size of the characteristic
set depends on the value of k, instead of the size of
an alphabet.