\begin{frame}{Exercise} \begin{exampleblock}{Question} \emph{Is the following language regular?} \begin{talign} \{\,a^n b^n \mid n \geq 0 \,\} \end{talign} \pause \alert{This language is not regular!} \pause\medskip \emph{Intuition:} a DFA has only a finite memory (the states). \end{exampleblock} We will later prove this using the \emph{pumping lemma}. % \begin{exampleblock}{} % Give a deterministic automaton with \emph{infinitely} many states for % \begin{align*} % \{\, a^n b^n \mid n \geq 0 \,\} % \end{align*} % \pause % Answer in the lecture. % \end{exampleblock} % \pause\medskip \end{frame}