First, I will present the question I was doing:
We will define $p(L)$ to be the minimal natural number so that a language L fulfill the pumping lemma.
We will also define $n(L)$ to be the minimal NFA (NFA with a minimal number of states) that accepts L.
Find a regular language so that $p(L)<n(L)$.
My solution: I will define $L$={$ab$,$cd$}, and ∑={$a,b,c,d$}.
The length of the longest word at L is 2 so it is easy to tell that $p(L)=3$.
Now, I don't think that exists a NFA with less states for $L$ then those two:
But I don't know how to formally prove that.
Maybe there is a possible connection here to an equivalent classes and DFA which might help?
Note: I am not allowed to use any algorithm for finding minimal automata (but I am allowed to use facts about equivalent classes and DFA).