1.1 --- a/slides/src/slides.tex	Wed Jul 20 03:03:50 2011 +0200
     1.2 +++ b/slides/src/slides.tex	Wed Jul 20 03:57:42 2011 +0200
     1.3 @@ -89,7 +89,7 @@
     1.4  
     1.5  \begin{frame}
     1.6  \frametitle{Automata}
     1.7 -\framesubtitle{Example 1/3}
     1.8 +\framesubtitle{Example 1/2}
     1.9  \begin{figure}
    1.10  \centering
    1.11  \only<1>{
    1.12 @@ -133,8 +133,10 @@
    1.13  (q_0) edge node {$a$} (q_1) 
    1.14  (q_1) edge node {$b$} (q_2);
    1.15  \draw[->] (q_2) .. controls +(up:1cm) and +(right:1cm) .. node[above] {$a$} (q_1);
    1.16 -\end{tikzpicture}
    1.17 +\end{tikzpicture}\\
    1.18  \color{black}
    1.19 +\vspace{20pt}
    1.20 +Accepts all inputs with infinite occurrences of $ab$.
    1.21  }
    1.22  %Automaton $\A_1$
    1.23  \end{figure}
    1.24 @@ -142,7 +144,7 @@
    1.25  
    1.26  \begin{frame}
    1.27  \frametitle{Automata}
    1.28 -\framesubtitle{Example 2/3 (Complement)}
    1.29 +\framesubtitle{Example 2/2 (Complement)}
    1.30  \begin{figure}
    1.31  \centering
    1.32  \only<-1>{
    1.33 @@ -236,8 +238,11 @@
    1.34                  (q_2) 
    1.35                  edge [loop above] node {$b$} ();
    1.36                \end{tikzpicture}\color{green}  
    1.37 -            }
    1.38 +            }\\
    1.39  \color{black}  
    1.40 +\vspace{20pt}
    1.41 +Accepts all inputs with infinite occurrences of $a$ or $b$.\\
    1.42 +Does \emph{not} accept inputs where both $a$ and $b$ occur infinitely often.
    1.43  }
    1.44  %\caption{Automata from Example \ref{ex:automaton}}
    1.45  \end{figure}
    1.46 @@ -280,7 +285,7 @@
    1.47  \begin{def:inf}
    1.48  Let $\A = (\Sigma, S, S_0, \Delta, F)$ be an automaton and let $\rho$ be a run of $\A$:
    1.49  \begin{itemize}
    1.50 -\item $\exists^\omega$ denotes the existential quantifier for infinitely many occurrences.
    1.51 +\item $\exists^\omega$ denotes the existential quantifier for \emph{infinitely} many occurrences.
    1.52  \item $inf(\rho) = \{s \in S \mid \exists^\omega{n \in \N}: \rho(n) = s\}$.
    1.53  \end{itemize}
    1.54  \end{def:inf}
    1.55 @@ -289,7 +294,7 @@
    1.56  Let $\A = (\Sigma, S, S_0, \Delta, F)$ be an automaton and let $\rho$ be a run of $\A$:
    1.57  \begin{itemize}
    1.58  \item $\rho$ is \emph{accepting} iff $inf(\rho) \cap F \neq \emptyset$.
    1.59 -\item $\A$ \emph{accepts} an input word $w$ iff there exists a run $\rho$ of $\A$ on $w$, such that $\rho$ is \emph{accepting}. 
    1.60 +\item $\A$ \emph{accepts} an input word $w$ iff there exists a run $\rho$ of $\A$ on $w$, such that $\rho$ is accepting. 
    1.61  \end{itemize}
    1.62  \end{def:automata acceptance}
    1.63  \end{frame}
    1.64 @@ -326,7 +331,7 @@
    1.65  Let $\A = (\Sigma, S, S_0, \Delta, \{F_i\}_{i<k})$ be a generalised automaton and let $\rho$ be a run of $\A$:
    1.66  \begin{itemize}
    1.67  \item $\rho$ is \emph{accepting} iff $\forall{i < k}: inf(\rho) \cap F_i \neq \emptyset$.
    1.68 -\item $\A$ \emph{accepts} an input word $w$ iff there exists a run $\rho$ of $\A$ on $w$, such that $\rho$ is \emph{accepting}. 
    1.69 +\item $\A$ \emph{accepts} an input word $w$ iff there exists a run $\rho$ of $\A$ on $w$, such that $\rho$ is accepting. 
    1.70  \end{itemize} 
    1.71  \end{def:general acceptance}
    1.72  \end{frame}