Binary file slides/slides04.pdf has changed

--- a/slides/slides04.tex	Mon Oct 13 06:30:09 2014 +0100
+++ b/slides/slides04.tex	Mon Oct 13 06:37:30 2014 +0100
@@ -620,7 +620,7 @@
 \begin{frame}[c]
 \frametitle{Mkeps}
 
-Finding a (posix) value for recognising the empty string
+Finding a (posix) value for recognising the empty string:
 
 \begin{center}
 \begin{tabular}{lcl}
@@ -672,6 +672,32 @@
 
 \footnotesize
 \bl{$lex$}: returns a value
+
+\begin{center}
+\begin{tikzpicture}[scale=2,node distance=1.0cm,every node/.style={minimum size=6mm}]
+\node (r1)  {\bl{$r_1$}};
+\node (r2) [right=of r1] {\bl{$r_2$}};
+\draw[->,line width=1mm]  (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};
+\node (r3) [right=of r2] {\bl{$r_3$}};
+\draw[->,line width=1mm]  (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};
+\node (r4) [right=of r3] {\bl{$r_4$}};
+\draw[->,line width=1mm]  (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};
+\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};
+\node (v4) [below=of r4] {\bl{$v_4$}};
+\draw[->,line width=1mm]  (r4) -- (v4);
+\node (v3) [left=of v4] {\bl{$v_3$}};
+\draw[->,line width=1mm]  (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};
+\node (v2) [left=of v3] {\bl{$v_2$}};
+\draw[->,line width=1mm]  (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};
+\node (v1) [left=of v2] {\bl{$v_1$}};
+\draw[->,line width=1mm]  (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};
+\draw[->,line width=0.5mm]  (r3) -- (v3);
+\draw[->,line width=0.5mm]  (r2) -- (v2);
+\draw[->,line width=0.5mm]  (r1) -- (v1);
+\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
+\end{tikzpicture}
+\end{center}
+
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
@@ -719,7 +745,7 @@
 \frametitle{Simplification}
 
 \begin{itemize}
-\item If we simplify after the derivative, then we ar builing the
+\item If we simplify after the derivative, then we are builing the
 value for the simplified regular expression, but \emph{not} for the original
 regular expression.
 \end{itemize}