I just came across an exercise which is to find a regular expression for the following automata, such that the regular expression and the automata generate the same language.
One solution presents the following expression:
$\qquad \displaystyle r_A = a^+b^+(c\mid ca^*b^+)^*$
However, can this be true? I think not, because the all words created from the regular expression will have at least one $b$ in it, whereas the automata accepts words without $b$, such as $aaa$.
What is your opinion?