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Journal Article
VC-dimensions of nondeterministic finite automata for words of equal length
2022
Overview
Let NFA
b
(
q
) denote the set of languages accepted by nondeterministic finite automata with
q
states over an alphabet with
b
letters. Let
B
n
denote the set of words of length
n
. We give a quadratic lower bound on the VC dimension of
NFA
2
(
q
)
∩
B
n
=
{
L
∩
B
n
∣
L
∈
NFA
2
(
q
)
}
as a function of
q
. Next, the work of Gruber and Holzer (Theoret. Comput. Sci.
387
(2): 155–166,
2007
) gives an upper bound for the nondeterministic state complexity of finite languages contained in
B
n
, which we strengthen using our methods. Finally, we give some theoretical and experimental results on the dependence on
n
of the VC dimension and testing dimension of NFA
2
(
q
) ∩
B
n
.
Publisher
Springer International Publishing,Springer,Springer Nature B.V
Subject
