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\begin{frame}{($\Rightarrow$) From NFA's to Regular Expressions (4)}
  \begin{construction}[$\Rightarrow$ continued]
    \emph{Step 4:}
    \smallskip
    
    If $F \neq \{q_0\}$, then the transition graph is finally of the form:
    \begin{center}\vspace{-1ex}
    \begin{tikzpicture}[default,node distance=20mm,->,s/.style={minimum size=5mm}]
      \node (q0) [state] {$q_0$}; \draw ($(q0) + (-8mm,0mm)$) -- (q0);
      \node (qf) [fstate,right of=q0] {}; 
  
      \draw (q0) to[bend left=20] node [above] {$r_2$} (qf);
      \draw (qf) to[bend left=20] node [below] {$r_3$} (q0);
      \draw (q0) to[tloop] node [above] {$r_1$} (q0);
      \draw (qf) to[tloop] node [above] {$r_4$} (qf);
    \end{tikzpicture}\vspace{-1.5ex}
    \end{center}
    \pause
    Possibly $r_1$, $r_2$, $r_3$ or $r_4$ are equal to $\emptyset$.
    \pause\medskip

    Then the regular expression is:
    \pause
    \begin{talign}
      \alert{L(r_1^*\cdot r_2\cdot (r_4 + r_3\cdot r_1^*\cdot r_2)^*)~=~L(M)}
    \end{talign}
  \end{construction}
  \pause

  \begin{question}
  What is the form of the transition graph and regular expression for the case that $F=\{q_0\}$\,?
  \end{question}
  \vspace{10cm}
\end{frame}