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

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

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

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  • $\begingroup$ But why is that so? Does that mean, that the RE is wrong? $\endgroup$
    – Momo
    Commented Oct 5, 2020 at 12:41
  • $\begingroup$ @Daisy Sure looks like it. $\endgroup$
    – Rick Decker
    Commented Oct 6, 2020 at 23:31

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