December 12th, 2015, 01:57 AM  #1 
Member Joined: Mar 2015 From: USA Posts: 34 Thanks: 1  Automata question
The question: Let it be $L$ a regular language. few definitions: $p(L)$the minimal natural number so that $L$ fulfill the pumping lemma. $n(L)$ minimal NFA that accepts $L$. $m(L)$ $Rank(L)$, the number of equivalence classes in $L$. Let it be integer $k>0$. find an example for a language $L$ so that: $p=n=m=k$. My attempt: At start, thought of $L=\{w: w\bmod k=0\}$, $\Sigma=\{ a\}$. But then I realized that $p<k$. And also for every $L$ that I choose here, I don't know how exactly to prove that the $NFA$ which accepts it is minimal. I know how to do this only on $NFA$'s with one or two states, but not on $NFA$'s with unknown number of states. How can I solve this? 

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