--- a/slides06.tex	Wed Oct 31 08:42:14 2012 +0000
+++ b/slides06.tex	Wed Oct 31 08:56:08 2012 +0000
@@ -376,7 +376,7 @@
 \begin{frame}[c]
 \frametitle{\begin{tabular}{c}Grammars\end{tabular}}
 
-A (context-free) Grammar \bl{$G$} consists of
+A (context-free) grammar \bl{$G$} consists of
 
 \begin{itemize}
 \item a finite set of nonterminal symbols (upper case)
@@ -407,8 +407,8 @@
 \begin{center}
 \bl{\begin{tabular}{lcl}
 $S$ & $\rightarrow$ &  $\epsilon$ \\
-$S$ & $\rightarrow$ &  $aSa$ \\
-$S$ & $\rightarrow$ &  $bSb$ \\
+$S$ & $\rightarrow$ &  $a\cdot S\cdot a$ \\
+$S$ & $\rightarrow$ &  $b\cdot S\cdot b$ \\
 \end{tabular}}
 \end{center}\pause
 
@@ -416,7 +416,7 @@
 
 \begin{center}
 \bl{\begin{tabular}{lcl}
-$S$ & $\rightarrow$ &  $\epsilon \;|\; aSa \;|\;bSb$ \\
+$S$ & $\rightarrow$ &  $\epsilon \;|\; a\cdot S\cdot a \;|\;b\cdot S\cdot b$ \\
 \end{tabular}}
 \end{center}
 
@@ -434,10 +434,10 @@
 \begin{center}
 \bl{\begin{tabular}{lcl}
 $E$ & $\rightarrow$ &  $num\_token$ \\
-$E$ & $\rightarrow$ &  $E + E$ \\
-$E$ & $\rightarrow$ &  $E - E$ \\
-$E$ & $\rightarrow$ &  $E * E$ \\
-$E$ & $\rightarrow$ &  $( E )$ 
+$E$ & $\rightarrow$ &  $E \cdot + \cdot E$ \\
+$E$ & $\rightarrow$ &  $E \cdot - \cdot E$ \\
+$E$ & $\rightarrow$ &  $E \cdot * \cdot E$ \\
+$E$ & $\rightarrow$ &  $( \cdot E \cdot )$ 
 \end{tabular}}
 \end{center}\pause
 
@@ -454,9 +454,9 @@
 
 \begin{center}
 \bl{\begin{tabular}{lcl}
-$E$ & $\rightarrow$ &  $F \;|\; F * F$\\
-$F$ & $\rightarrow$ & $T \;|\; T + T \;|\; T - T$\\
-$T$ & $\rightarrow$ & $num\_token \;|\; ( E )$\\
+$E$ & $\rightarrow$ &  $F \;|\; F \cdot * \cdot F$\\
+$F$ & $\rightarrow$ & $T \;|\; T \cdot + \cdot T \;|\; T \cdot - \cdot T$\\
+$T$ & $\rightarrow$ & $num\_token \;|\; ( \cdot E \cdot )$\\
 \end{tabular}}
 \end{center}
 
@@ -502,10 +502,10 @@
 \begin{center}
 \bl{\begin{tabular}{lcl}
 $E$ & $\rightarrow$ &  $num\_token$ \\
-$E$ & $\rightarrow$ &  $E + E$ \\
-$E$ & $\rightarrow$ &  $E - E$ \\
-$E$ & $\rightarrow$ &  $E * E$ \\
-$E$ & $\rightarrow$ &  $( E )$ 
+$E$ & $\rightarrow$ &  $E \cdot + \cdot E$ \\
+$E$ & $\rightarrow$ &  $E \cdot - \cdot E$ \\
+$E$ & $\rightarrow$ &  $E \cdot * \cdot E$ \\
+$E$ & $\rightarrow$ &  $( \cdot E \cdot )$ 
 \end{tabular}}
 \end{center}
 
@@ -529,14 +529,33 @@
 or
 
 \begin{center}
-\bl{$A \rightarrow BC$}
+\bl{$A \rightarrow B\cdot C$}
 \end{center}
 
 
 
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}}
 
+
+\begin{center}
+\bl{\begin{tabular}{@ {}lcl}
+$S$ & $\rightarrow$ &  $N\cdot P$ \\
+$P$ & $\rightarrow$ &  $V\cdot N$ \\
+$N$ & $\rightarrow$ &  $N\cdot N$ \\
+$N$ & $\rightarrow$ &  $\texttt{students} \;|\; \texttt{Jeff} \;|\; \texttt{geometry} \;|\; \texttt{trains} $ \\
+$E$ & $\rightarrow$ &  $\texttt{trains}$ 
+\end{tabular}}
+\end{center}
+
+\bl{\texttt{Jeff trains geometry students}}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]