\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}