--- a/slides/slides03.tex	Sun Oct 12 12:50:16 2025 +0100
+++ b/slides/slides03.tex	Fri Oct 17 11:20:49 2025 +0100
@@ -65,20 +65,42 @@
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-{
-\setbeamercolor{background canvas}{bg=cream}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{For Installation Problems}
+
+\begin{mybox3}{From Mentimeter}\it    
+Is there a specific reason Python and the other programming 
+languages have not implemented their regex matcher like the much 
+faster algorithms described in the videos?
+\end{mybox3}  
+
+\begin{mybox3}{From the Survey}\it    
+If worst case for regex with derivatives is same as a
+normal regex engine, why is there a heavy focus on regex
+for lexer given most languages don't use it.
+\end{mybox3}  
 
-\begin{itemize}
-\item Harry Dilnot (harry.dilnot@kcl.ac.uk) \\
-  \;\;Windows expert
-\item Oliver Iliffe (oliver.iliffe@kcl.ac.uk) 
-\end{itemize}
-  
 \end{frame}
-}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+%{
+%\setbeamercolor{background canvas}{bg=cream}
+%\begin{frame}[c]
+%\frametitle{For Installation Problems}
+%
+%\begin{itemize}
+%\item Harry Dilnot (harry.dilnot@kcl.ac.uk) \\
+%  \;\;Windows expert
+%\item Oliver Iliffe (oliver.iliffe@kcl.ac.uk) 
+%\end{itemize}
+%  
+%\end{frame}
+%}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -193,16 +215,16 @@
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-
-\begin{mybox3}{From Pollev last week}\it    
-  For a regular expression $r = r_1 \cdot r_2$, to prove that
-  $der\;c\;r = (der\;c\;r) \cdot r^{\{n-1\}}$, is there a
-  way to prove it in the general case instead
-  of how you do the calculations for each $n$ in the videos?
-\end{mybox3}  
-
-\end{frame}
+%\begin{frame}[c]
+%
+%\begin{mybox3}{From Pollev last week}\it    
+%  For a regular expression $r = r_1 \cdot r_2$, to prove that
+%  $der\;c\;r = (der\;c\;r) \cdot r^{\{n-1\}}$, is there a
+%  way to prove it in the general case instead
+%  of how you do the calculations for each $n$ in the videos?
+%\end{mybox3}  
+%
+%\end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
@@ -1621,6 +1643,8 @@
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
+ 
+
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %\begin{frame}[c]
@@ -1842,6 +1866,31 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
+\frametitle{Hierarchy of Languages}
+
+\begin{center}
+\begin{tikzpicture}
+[rect/.style={draw=black!50, 
+              top color=white,
+              bottom color=black!20, 
+              rectangle, 
+              very thick, 
+              rounded corners}, scale=1.2]
+
+\draw (0,0) node [rect, text depth=39mm, text width=68mm] {all languages};
+\draw (0,-0.4) node [rect, text depth=28.5mm, text width=64mm] {decidable languages};
+\draw (0,-0.85) node [rect, text depth=17mm] {context sensitive languages};
+\draw (0,-1.14) node [rect, text depth=9mm, text width=50mm] {context-free languages};
+\draw (0,-1.4) node [rect] {regular languages};
+\end{tikzpicture}
+
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
 \frametitle{Negation}
 
 Regular languages are closed under negation:\bigskip