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\begin{frame}{Turing Machine Configuration}
So configurations are denoted by words from $\Gamma^* \times Q \times \Gamma^*$.
\begin{exampleblock}{}
For instance, the configuration
\begin{center}
\def\cellwidth{10mm}
\def\cellheight{6mm}
\def\cellfrom{-3}
\def\cellto{3}
\begin{tikzpicture}[default,-,thin]
\draw [draw=none,fill=orange!15] (\cellfrom*\cellwidth - \cellwidth,\cellheight/2) rectangle (\cellto*\cellwidth + \cellwidth,-\cellheight/2);

\foreach \i in {\cellfrom,...,\cellto} {
\draw ({\cellwidth*(\i-0.5)},\cellheight/2) -- ({\cellwidth*(\i-0.5)},-\cellheight/2);
\node (cell\i) at ({\cellwidth*\i},0) {};
}
\draw ({\cellwidth*(\cellto+0.5)},\cellheight/2) -- ({\cellwidth*(\cellto+0.5)},-\cellheight/2);

\draw (\cellfrom*\cellwidth - \cellwidth,\cellheight/2) -- (\cellto*\cellwidth + \cellwidth,\cellheight/2);
\draw (\cellfrom*\cellwidth - \cellwidth,-\cellheight/2) -- (\cellto*\cellwidth + \cellwidth,-\cellheight/2);

\node [anchor=east] at (\cellfrom*\cellwidth - \cellwidth,0) {$\dots$};
\node [anchor=west] at (\cellto*\cellwidth + \cellwidth,0) {$\dots$};

\node (cu) [rectangle,rounded corners=2mm,draw,inner sep=2mm,fill=orange!15] at ($(cell0) + (0,2*\cellheight)$) {$q$};
\draw [<->] (cu) to ($(cell0) + (0,\cellheight/2)$);

\foreach \i/\t in {-3/\Box,-2/e,-1/d,0/a,1/b,2/b,3/\Box} {
\node [scale=0.9] at (cell\i) {$\t$};
}
\end{tikzpicture}\vspace{-1ex}
\end{center}
can be denoted by
\begin{talign}
ed\,q\,abb
\end{talign}
\pause
The words
\begin{talign}
ed\,q\,abb\Box &&\mpause[1]{\approx}&&
\Box ed\,q\,abb &&\mpause[1]{\approx}&&
\Box\Box ed\,q\,abb \Box && \cdots
\end{talign}
denote the same configuration.
\end{exampleblock}
\pause

\begin{goal}{}
We write $w \approx v$ if $w$ and $v$ denote the same configuration.
\end{goal}
\end{frame}