# No nonfinal states in NFA

I know that if there are no non-final states in DFA then the language accepted is $$\Sigma^*$$.

What will happen if there are no non-final states in an NFA? Can we say it also accepts $$\Sigma^*$$? Can there be an NFA with no non-final states whose minimal NFA has some non-final state?

Oh , no nonfinal states means all are final states. So DFA - all final states means every string gets accepted. So language is $$\sum^*$$. For NFA, it need not be $$\sum^*$$. Please correct me if i am wrong here. Other case --> If there are no final states(all non-final states) means in DFA, language accepted is empty language. In case of NFA with no final state means empty language right?

• Do you know why a DFA with no non-final states accepts $\Sigma^*$? See if the same argument works in your case. – Yuval Filmus Nov 12 '19 at 16:52
• I don't see where minimal automata enter the picture. The definition of the language accepted by a DFA/NFA doesn't involve them. – Yuval Filmus Nov 12 '19 at 17:04
• Can you give an example of an NFA with no non-final states whose language is not everything? – Yuval Filmus Nov 12 '19 at 19:41
• Yes, seems fine. – Yuval Filmus Nov 12 '19 at 20:08
• I think I gave you enough help. – Yuval Filmus Nov 12 '19 at 20:11

This NFA accepts the language $$\{\varepsilon\}$$—that is, only the empty string. If it is given a non-empty string, it looks for appropriate edges leading away from the starting state, finds none, and fails.