--- a/slides/slides02.tex	Sat Sep 24 08:47:25 2016 +0100
+++ b/slides/slides02.tex	Sat Oct 01 22:30:51 2016 +0100
@@ -144,7 +144,7 @@
 
 \begin{center}
 \begin{tabular}{lcl}
-\bl{$A^0$}     & \bl{$\dn$} & \bl{$\{[]\}$}\\
+\bl{$A^0$}    & \bl{$\dn$} & \bl{$\{[]\}$}\\
 \bl{$A^{n+1}$} & \bl{$\dn$} & \bl{$A \,@\, A^n$}
 \end{tabular}
 \end{center}\bigskip
@@ -152,9 +152,10 @@
 \item[] For example
 
 \begin{center}
-\begin{tabular}{l}
-\bl{$A^4 = A \,@\, A \,@\, A \,@\, A$}\\
-\bl{$A^0 \dn \{[]\}$}\\
+\begin{tabular}{lcl}
+\bl{$A^4$} & \bl{$=$} & \bl{$A \,@\, A \,@\, A \,@\, A$}\\
+\bl{$A^1$} & \bl{$=$} & \bl{$A$}\\
+\bl{$A^0$} & \bl{$=$} & \bl{$\{[]\}$}\\
 \end{tabular}
 \end{center}
 
@@ -196,7 +197,7 @@
 
 \begin{center}
 \begin{tabular}{c}
-\bl{$A^* \dn \bigcup_{0\le n} A^n$}
+\bl{$A\star \dn \bigcup_{0\le n} A^n$}
 \end{tabular}
 \end{center}\bigskip
 
@@ -291,7 +292,7 @@
  \bl{$L(c)$}               & \bl{$\dn$} & \bl{$\{[c]\}$}\\
  \bl{$L(r_1 + r_2)$}       & \bl{$\dn$} & \bl{$L(r_1) \cup L(r_2)$}\\
  \bl{$L(r_1 \cdot r_2)$}   & \bl{$\dn$} & \bl{$L(r_1) \,@\, L(r_2)$}\\
- \bl{$L(r^*)$}             & \bl{$\dn$} & \bl{$(L(r))^*$}\\
+ \bl{$L(r^*)$}             & \bl{$\dn$} & \bl{$(L(r))\star$}\\
  \end{tabular}
 \end{textblock}
 
@@ -403,7 +404,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{\bl{$({a^?}^{\{n\}}) \cdot a^{\{n\}}$}}
+\frametitle{\bl{$(a^{?\{n\}}) \cdot a^{\{n\}}$}}
 
 \begin{center}
 \begin{tikzpicture}
@@ -442,7 +443,7 @@
 \item \alert{R}egular \alert{e}xpression \alert{D}enial \alert{o}f \alert{S}ervice (ReDoS)\bigskip
 \item Evil regular expressions\medskip
 \begin{itemize}
-\item \bl{$({a^?}^{\{n\}}) \cdot a^{\{n\}}$}
+\item \bl{$(a^{?\{n\}}) \cdot a^{\{n\}}$}
 \item \bl{$(a^+)^+$}
 \item \bl{$([a$\,-\,$z]^+)^*$}
 \item \bl{$(a + a \cdot a)^+$}
@@ -528,6 +529,20 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
+\frametitle{The Algorithm}
+
+\begin{center}
+\begin{tabular}{l}
+\bl{$\textit{matches}\,r\,s \dn \textit{nullable}(\textit{ders}\,r\,s)$}  
+\end{tabular}
+\end{center}
+
+
+\end{frame}
+%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
 \frametitle{The Algorithm}
 
@@ -572,7 +587,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{\bl{$({a^?}^{\{n\}}) \cdot a^{\{n\}}$}}
+\frametitle{\bl{$(a^{?\{n\}}) \cdot a^{\{n\}}$}}
 
 \begin{center}
 \begin{tikzpicture}
@@ -649,7 +664,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-\frametitle{\bl{$({a^?}^{\{n\}}) \cdot a^{\{n\}}$}}
+\frametitle{\bl{$(a^{?\{n\}}) \cdot a^{\{n\}}$}}
 
 \begin{center}
 \begin{tikzpicture}
@@ -707,7 +722,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-\frametitle{\bl{$({a^?}^{\{n\}}) \cdot a^{\{n\}}$}}
+\frametitle{\bl{$(a^{?\{n\}}) \cdot a^{\{n\}}$}}
 
 \begin{center}
 \begin{tikzpicture}