\begin{frame}{NFAs Reading Words}
  Let $M = (Q,\Sigma,\delta,S,F)$ be a NFA. 
  %   \begin{block}{}
  %     A \emph{configuration} of $M$ is a pair $(q,w)$ with $q \in Q$ and $w \in \Sigma^*$.
  %   \end{block}
  \begin{block}{}
    The \emph{step relation $\vdash$} of $M$ is defined on configurations by 
    \begin{talign}
      (q,\alert{\alpha} w) \vdash (q',w) \quad \text{if $\alert{q' \in} \delta(q,\alert{\alpha})$ with $\alpha \in \Sigma \alert{\cup\{\lambda\}}$}
    \end{talign}
  \end{block}

  \pause
  Note that if $\alpha = \lambda$, then 
  \begin{itemize}
    \item the state changes ($q$ to $q'$), but
    \item the input word stays the same ($\lambda w = w$).
  \end{itemize}
  \pause\medskip

  \begin{exampleblock}{}
    \begin{center}
      \vspace{-.5ex}
      \input{tikz/nfa1.tex}
      \vspace{-1.5ex}
    \end{center}
    \begin{talign}
      (q_0,abbab) 
        &\vdash (q_1,bbab) \vdash (q_1,bab) \vdash (q_2,ab) \\ 
        &\vdash (q_0,b) \vdash (q_1,b) \vdash (q_1,\lambda)
    \end{talign}
  \end{exampleblock}    
\end{frame}