\begin{frame}{Exercise: DFA Minimisation}
  \begin{exampleblock}{}
    \begin{center}
      \input{tikz/dfa2.tex}
    \end{center}\vspace{-2ex}
    \begin{enumerate}
      \item [2.] Final partitioning: $\{\, \{\, q_0 \,\}, \{\, q_1, q_2 \,\}, \{\, q_3 \,\}, \{\, q_4 \,\} \,\}$.
    \pause 
      \item [3.] Reading off the minimal DFA:
    \begin{center}
      \begin{tikzpicture}[default,node distance=20mm,->]
        \node (q0) [state] {$\{q_0\}$}; \draw ($(q0) + (-10mm,0mm)$) -- (q0); 
        \node (q2) [right of=q0] {};
        \node (q4) [fstate,right of=q2] {$\{q_4\}$};
        \begin{scope}[node distance=15mm]
        \node (q1) [state,above of=q2,node distance=10mm] {$\{q_1,q_2\}$};
        \node (q3) [state,below of=q2,node distance=10mm] {$\{q_3\}$};
        \end{scope}
        
        \draw (q0) to node [label,above left] {$a$} (q1);
        \draw (q0) to[bend left=10] node [label,above right] {$b$} (q3);
        \draw (q1) to[bloop] node [label,below] {$a$} (q1);
        \draw (q1) to node [label,above right] {$b$} (q4);
        \draw (q3) to[bend left=10] node [label,below left] {$a$} (q0);
        \draw (q3) to[bend left=10] node [label,above left] {$b$} (q4);
        \draw (q4) to[bend left=10] node [label,below right] {$a$} (q3);
        \draw (q4) to[rloop] node [label,right] {$b$} (q4);
      \end{tikzpicture}
    \end{center}
    \end{enumerate}
  \end{exampleblock}
  \vspace{10cm}
\end{frame}