\begin{frame}{Universal Turing Machine} A computer can execute any program on any input. \medskip\pause \begin{goal}{} A TM is called \emph{universal} if it can simulate every TM. \medskip A universal TM gets as input \begin{itemize} \item a Turing machine $M$ (described as a word $w$) \item an input word $u$ \end{itemize} and then executes (simulates) $M$ on $u$. \end{goal} The input $w$ and $u$ can be written on the tape as $w\#u$. \medskip\pause \begin{block}{Theorem} There exists a universal Turing machine. \end{block} \end{frame}