--- a/slides/slides02.tex	Wed Oct 07 09:08:55 2020 +0100
+++ b/slides/slides02.tex	Sun Oct 11 09:10:08 2020 +0100
@@ -866,6 +866,38 @@
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t]
+\frametitle{Brzozowski: \boldmath$a^{?\{n\}} \cdot a^{\{n\}}$}
+
+\begin{center}
+\begin{tikzpicture}
+\begin{axis}[
+    xlabel={$n$},
+    x label style={at={(1.05,0.0)}},     
+    ylabel={time in secs},
+    enlargelimits=false,
+    xtick={0,5000,...,10000},
+    xmax=11000,
+    ymax=35,
+    ytick={0,5,...,30},
+    scaled ticks=false,
+    axis lines=left,
+    width=9cm,
+    height=7cm,
+    legend entries={Scala V2,Scala V3,Rust},  
+    legend pos=north east
+]
+\addplot[green,mark=square*,mark options={fill=white}] table {re2.data};
+\addplot[black,mark=square*,mark options={fill=white}] table {re3.data};
+\addplot[pink,mark=triangle,mark options={fill=pink}] table {re-rust.data};
+\end{axis}
+\end{tikzpicture}
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
@@ -888,7 +920,7 @@
     width=9cm,
     height=5.5cm, 
     legend entries={Java 8,Python,JavaScript,Swift,Dart},  
-    legend pos=north west,
+    legend pos=outer north east,
     legend cell align=left]
 \addplot[blue,mark=*, mark options={fill=white}] table {re-python2.data};
 \addplot[cyan,mark=*, mark options={fill=white}] table {re-java.data};
@@ -1110,6 +1142,56 @@
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
+\begin{frame}[c]
+\begin{mybox3}{}
+  der c (r*) def = (der c r) $\cdot$ (r*)\smallskip\\
+  Why in the example (slide 19) the first step is:
+  der a ((a $\cdot$ b) + b)* = (der a ((a $\cdot$ b) + b)) $\cdot$ r\smallskip\\
+  and not\smallskip\\
+  der a ((a $\cdot$ b) + b) = (der a ((a $\cdot$ b) + b)) · (r*)
+\end{mybox3}
+\end{frame}
+
+\begin{frame}[c]
+\begin{mybox3}{}
+  Would it be possible to find and go over a few examples from the
+  Brzozowski Algorithm, as it doesn't seem to be as simple as it
+  sounds?
+\end{mybox3}
+\end{frame}
+
+\begin{frame}[c]
+\begin{mybox3}{}
+  Is it possible to make a visual example of how using simp() function
+  on a (a*)*.b regular expression reduces its runtime? If not it's
+  fine. I am just very surprised that it is so efficient.
+\end{mybox3}
+\end{frame}
+
+\begin{frame}[c]
+\begin{mybox3}{}
+  Do you think the algorithm can be still improved (made faster)?
+\end{mybox3}
+\end{frame}
+
+\begin{frame}[c]
+\begin{mybox3}{}
+  Do the regular expression matchers in Python and Java 8 have more
+  features than the one implemented in this module? Or is there
+  another reason for their inefficiency?
+\end{mybox3}
+\end{frame}
+
+\begin{frame}[c]
+\begin{mybox3}{}
+  Will we discuss the broader Chomsky hierarchy of languages at some
+  point?
+\end{mybox3}
+\end{frame}
+
+\begin{frame}<1-8>[c]
+\end{frame}
+
 \end{document}
 % below are slides for proving.