\begin{frame}{Motivation}
  Different kinds of automata for different applications.
  \begin{center}
    \vspace{-1ex}
    \begin{tikzpicture}[default,label/.style={rectangle,inner sep=0.5mm}]
      \amorse
    \end{tikzpicture}
    \vspace{-1ex}
  \end{center}
  
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  \begin{goal}{}
    \emph{Finite automata} give rise to regular languages:
    \begin{itemize}
      \item application: \emph{pattern recognition}
      \item equivalent to: \emph{regular expressions}, regular grammars  
    \end{itemize}
  \end{goal}

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  \begin{goal}{}
    \emph{Pushdown automata} give rise to context-free languages:
    \begin{itemize}
      \item application: \emph{parsing} (e.g. programming languages)
      \item equivalent to context-free grammars
    \end{itemize}
  \end{goal}
  
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  \begin{goal}{}
    \emph{Turing machines} yield recursively enumerable languages:
    \begin{itemize}
      \item application: general \emph{computation}
    \end{itemize} 
  \end{goal}
\end{frame}