\begin{frame}{Turing Machines}
  \begin{goal}{}
    A \emph{deterministic Turing machine}, short TM, is a 7-tuple 
    \begin{talign}
      (Q,\Sigma,\Gamma,\delta,q_0,\Box,F)
    \end{talign}
    where
    \begin{itemize}
      \item \alert{$Q$} is a finite set of states,
      \item $\alert{\Sigma} \subseteq \Gamma \setminus \{\,\Box\,\}$ a finite input alphabet,
      \item \alert{$\Gamma$} a finite tape alphabet,
      \item $\alert{\delta} : Q \times \Gamma \to Q \times \Gamma \times \{\,L,R\,\}$ a partial transition function,
      \item \alert{$q_0$} the starting state,
      \item $\alert{\Box} \in \Gamma$ the blank symbol,
      \item $\alert{F} \subseteq Q$ a set of final (accepting) states.
    \end{itemize}
  \end{goal}
  \pause
  
  \begin{block}{}
    \emph{Assumption}: $\delta(q,a)$ is undefined for every $q\in F$ and $a\in\Gamma$.
  \end{block}
  So the computation stops when reaching a final state.
\end{frame}