# Read regular Expression from NFA

Good evening everyone! Can someone help me with the following task? So we have this NFA:

I was supposed to create a regular expression out of it. Now the solution says: $$a^{+}b^{+}(c|ca^{*}b^{+})^{*}$$ Unfortunately I don't understand how this is possible. If I look at the NFA, then we can accept a word that only includes one a without any b's. But the regular expression in the solution does not make that possible. Or am I missing something? I also converted the NFA to a DFA however that didn't help much.

Thanks!

The RE is wrong. It also includes abcb which is not in the language of the automaton.

The direct edge (a) from initial state 1 to final state 3 is not included in the RE.

• But why is that so? Does that mean, that the RE is wrong? Oct 5 '20 at 12:41
• @Daisy Sure looks like it. Oct 6 '20 at 23:31