\begin{frame}
  \frametitle{Drawing Turing Machines}

  \begin{goal}{}
    The transition graph for a TMs contains 
    \begin{talign}
      \text{an arrow \quad \alert{$q \stackrel{a/b\text{ }X}{\longrightarrow} q'$} \quad}
      \text{whenever \quad \alert{$\delta(q,a) = (q',b,X)$}}
    \end{talign}
  \end{goal}
  
  \begin{exampleblock}{}
    The Turing machine $M = (Q,\Sigma,\Gamma,\delta,q_0,\Box,F)$ with 
    $\Sigma = \{\, a,b \,\}$,
    $\Gamma = \{\, a,b,\Box \,\}$,
    $Q = \{\, q_0,q_1,q_2 \,\}$,
    $F = \{\, q_2 \,\}$ and
    \begin{talign}
      \delta(q_0,a) &= (q_1,b,R) &
      \delta(q_1,a) &= (q_0,b,R) 
      \\
      \delta(q_0,b) &= (q_0,a,R) &
      \delta(q_1,b) &= (q_1,a,R) 
      \\
      &&
      \delta(q_1,\Box) &= (q_2,\Box,L) 
    \end{talign}
    can be visualised as
    \begin{center}
      \begin{tikzpicture}[default,node distance=25mm,->,s/.style={minimum size=5mm}]
        \node (q0) [state,s] {$q_0$}; \draw ($(q0) + (-8mm,0mm)$) -- (q0); 
        \node (q1) [state,s,right of=q0] {$q_1$};
        \node (q2) [fstate,s,right of=q1] {$q_2$};
      
        \draw (q0) to[bend left=20] node [label,above] {$a/b$ $R$} (q1);
        \draw (q0) to[tloop] node [label,above] {$b/a$ $R$} (q0);
        \draw (q1) to[bend left=20] node [label,below] {$a/b$ $R$} (q0);
        \draw (q1) to[tloop] node [label,above] {$b/a$ $R$} (q1);
        \draw (q1) to node [label,above] {$\Box/\Box$ $L$} (q2);
      \end{tikzpicture}
    \end{center}
  \end{exampleblock}  

\end{frame}