I would appreciate some help for the following exercise:
$L$ is a regular language if and only if there is a "reduced" NFA $N=\langle Q,A,\Delta, q_0,F\rangle$ with $L=L(N)$.
With reduced I mean the following property: $\forall q \in Q \exists u, v \in A^* \exists q_f\in F : (q_0,u,q)\in \Delta$ and $(q,v,q_f)\in \Delta$
My problem is to show that there is such a NFA if $L$ is regular. I know I can assume that there is a NFA which accepts the language so my idea was to use the pumping lemma to construct a reduced NFA with it. Can someone give me a hint on how to approach this exercise?