
diff -r 955d5b3b0619 -r 2849c305b12d slides/slides04.tex
--- a/slides/slides04.tex	Sun Oct 15 20:47:14 2017 +0100
+++ b/slides/slides04.tex	Tue Oct 17 13:49:45 2017 +0100
@@ -86,141 +86,141 @@
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{DFA to Rexp}
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \begin{frame}[c]
+% \frametitle{DFA to Rexp}
 
-\begin{center}
-\begin{tikzpicture}[scale=2,>=stealth',very thick,
-                    every state/.style={minimum size=0pt,
-                    draw=blue!50,very thick,fill=blue!20},]
-  \node[state, initial]        (q0) at ( 0,1) {$q_0$};
-  \node[state]                    (q1) at ( 1,1) {$q_1$};
-  \node[state, accepting] (q2) at ( 2,1) {$q_2$};
-  \path[->] (q0) edge[bend left] node[above] {\alert{$a$}} (q1)
-            (q1) edge[bend left] node[above] {\alert{$b$}} (q0)
-            (q2) edge[bend left=50] node[below] {\alert{$b$}} (q0)
-            (q1) edge node[above] {\alert{$a$}} (q2)
-            (q2) edge [loop right] node {\alert{$a$}} ()
-            (q0) edge [loop below] node {\alert{$b$}} ();
-\end{tikzpicture}
-\end{center}\bigskip
+% \begin{center}
+% \begin{tikzpicture}[scale=2,>=stealth',very thick,
+%                     every state/.style={minimum size=0pt,
+%                     draw=blue!50,very thick,fill=blue!20},]
+%   \node[state, initial]        (q0) at ( 0,1) {$q_0$};
+%   \node[state]                    (q1) at ( 1,1) {$q_1$};
+%   \node[state, accepting] (q2) at ( 2,1) {$q_2$};
+%   \path[->] (q0) edge[bend left] node[above] {\alert{$a$}} (q1)
+%             (q1) edge[bend left] node[above] {\alert{$b$}} (q0)
+%             (q2) edge[bend left=50] node[below] {\alert{$b$}} (q0)
+%             (q1) edge node[above] {\alert{$a$}} (q2)
+%             (q2) edge [loop right] node {\alert{$a$}} ()
+%             (q0) edge [loop below] node {\alert{$b$}} ();
+% \end{tikzpicture}
+% \end{center}\bigskip
 
-\begin{center}
-\begin{tabular}{r@ {\hspace{2mm}}c@ {\hspace{2mm}}l@{\hspace{7mm}}l}
-\bl{$q_0$} & \bl{$=$} & \bl{$\ONE + q_0\,b + q_1\,b +  q_2\,b$} & (start state)\\
-\bl{$q_1$} & \bl{$=$} & \bl{$q_0\,a$}\\
-\bl{$q_2$} & \bl{$=$} & \bl{$q_1\,a + q_2\,a$}\\
+% \begin{center}
+% \begin{tabular}{r@ {\hspace{2mm}}c@ {\hspace{2mm}}l@{\hspace{7mm}}l}
+% \bl{$q_0$} & \bl{$=$} & \bl{$\ONE + q_0\,b + q_1\,b +  q_2\,b$} & (start state)\\
+% \bl{$q_1$} & \bl{$=$} & \bl{$q_0\,a$}\\
+% \bl{$q_2$} & \bl{$=$} & \bl{$q_1\,a + q_2\,a$}\\
 
-\end{tabular}
-\end{center}
+% \end{tabular}
+% \end{center}
 
-Arden's Lemma:
-\begin{center}
-If \bl{$q = q\,r + s$}\; then\; \bl{$q = s\, r^*$}
-\end{center}
+% Arden's Lemma:
+% \begin{center}
+% If \bl{$q = q\,r + s$}\; then\; \bl{$q = s\, r^*$}
+% \end{center}
 
 
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+% \end{frame}
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{DFA Minimisation}
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \begin{frame}[c]
+% \frametitle{DFA Minimisation}
 
-\begin{enumerate}
-\item Take all pairs \bl{$(q, p)$} with \bl{$q \not= p$}
-\item Mark all pairs that accepting and non-accepting states
-\item For  all unmarked pairs \bl{$(q, p)$} and all characters \bl{$c$} test whether
-\begin{center}
-\bl{$(\delta(q, c), \delta(p,c))$}
-\end{center} 
-are marked. If yes, then also mark \bl{$(q, p)$}.
-\item Repeat last step until no change.
-\item All unmarked pairs can be merged.
-\end{enumerate}
+% \begin{enumerate}
+% \item Take all pairs \bl{$(q, p)$} with \bl{$q \not= p$}
+% \item Mark all pairs that accepting and non-accepting states
+% \item For  all unmarked pairs \bl{$(q, p)$} and all characters \bl{$c$} test whether
+% \begin{center}
+% \bl{$(\delta(q, c), \delta(p,c))$}
+% \end{center} 
+% are marked. If yes, then also mark \bl{$(q, p)$}.
+% \item Repeat last step until no change.
+% \item All unmarked pairs can be merged.
+% \end{enumerate}
 
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+% \end{frame}
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \begin{frame}[c]
 
-\begin{center}
-\begin{tabular}{@{\hspace{-8mm}}cc@{}}
-\begin{tikzpicture}[>=stealth',very thick,auto,
-                             every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
-\node[state,initial]  (q_0)  {$q_0$};
-\node[state] (q_1) [right=of q_0] {$q_1$};
-\node[state] (q_2) [below right=of q_0] {$q_2$};
-\node[state] (q_3) [right=of q_2] {$q_3$};
-\node[state, accepting] (q_4) [right=of q_1] {$q_4$};
-\path[->] (q_0) edge node [above]  {\alert{$a$}} (q_1);
-\path[->] (q_1) edge node [above]  {\alert{$a$}} (q_4);
-\path[->] (q_4) edge [loop right] node  {\alert{$a, b$}} ();
-\path[->] (q_3) edge node [right]  {\alert{$a$}} (q_4);
-\path[->] (q_2) edge node [above]  {\alert{$a$}} (q_3);
-\path[->] (q_1) edge node [right]  {\alert{$b$}} (q_2);
-\path[->] (q_0) edge node [above]  {\alert{$b$}} (q_2);
-\path[->] (q_2) edge [loop left] node  {\alert{$b$}} ();
-\path[->] (q_3) edge [bend left=95, looseness=1.3] node [below]  {\alert{$b$}} (q_0);
-\end{tikzpicture}
-&
-\raisebox{9mm}{\begin{tikzpicture}[scale=0.6,line width=0.8mm]
-\draw (0,0) -- (4,0);
-\draw (0,1) -- (4,1);
-\draw (0,2) -- (3,2);
-\draw (0,3) -- (2,3);
-\draw (0,4) -- (1,4);
+% \begin{center}
+% \begin{tabular}{@{\hspace{-8mm}}cc@{}}
+% \begin{tikzpicture}[>=stealth',very thick,auto,
+%                              every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
+% \node[state,initial]  (q_0)  {$q_0$};
+% \node[state] (q_1) [right=of q_0] {$q_1$};
+% \node[state] (q_2) [below right=of q_0] {$q_2$};
+% \node[state] (q_3) [right=of q_2] {$q_3$};
+% \node[state, accepting] (q_4) [right=of q_1] {$q_4$};
+% \path[->] (q_0) edge node [above]  {\alert{$a$}} (q_1);
+% \path[->] (q_1) edge node [above]  {\alert{$a$}} (q_4);
+% \path[->] (q_4) edge [loop right] node  {\alert{$a, b$}} ();
+% \path[->] (q_3) edge node [right]  {\alert{$a$}} (q_4);
+% \path[->] (q_2) edge node [above]  {\alert{$a$}} (q_3);
+% \path[->] (q_1) edge node [right]  {\alert{$b$}} (q_2);
+% \path[->] (q_0) edge node [above]  {\alert{$b$}} (q_2);
+% \path[->] (q_2) edge [loop left] node  {\alert{$b$}} ();
+% \path[->] (q_3) edge [bend left=95, looseness=1.3] node [below]  {\alert{$b$}} (q_0);
+% \end{tikzpicture}
+% &
+% \raisebox{9mm}{\begin{tikzpicture}[scale=0.6,line width=0.8mm]
+% \draw (0,0) -- (4,0);
+% \draw (0,1) -- (4,1);
+% \draw (0,2) -- (3,2);
+% \draw (0,3) -- (2,3);
+% \draw (0,4) -- (1,4);
 
-\draw (0,0) -- (0, 4);
-\draw (1,0) -- (1, 4);
-\draw (2,0) -- (2, 3);
-\draw (3,0) -- (3, 2);
-\draw (4,0) -- (4, 1);
+% \draw (0,0) -- (0, 4);
+% \draw (1,0) -- (1, 4);
+% \draw (2,0) -- (2, 3);
+% \draw (3,0) -- (3, 2);
+% \draw (4,0) -- (4, 1);
 
-\draw (0.5,-0.5) node {$q_0$}; 
-\draw (1.5,-0.5) node {$q_1$}; 
-\draw (2.5,-0.5) node {$q_2$}; 
-\draw (3.5,-0.5) node {$q_3$};
+% \draw (0.5,-0.5) node {$q_0$}; 
+% \draw (1.5,-0.5) node {$q_1$}; 
+% \draw (2.5,-0.5) node {$q_2$}; 
+% \draw (3.5,-0.5) node {$q_3$};
  
-\draw (-0.5, 3.5) node {$q_1$}; 
-\draw (-0.5, 2.5) node {$q_2$}; 
-\draw (-0.5, 1.5) node {$q_3$}; 
-\draw (-0.5, 0.5) node {$q_4$}; 
+% \draw (-0.5, 3.5) node {$q_1$}; 
+% \draw (-0.5, 2.5) node {$q_2$}; 
+% \draw (-0.5, 1.5) node {$q_3$}; 
+% \draw (-0.5, 0.5) node {$q_4$}; 
 
-\draw (0.5,0.5) node {\large$\star$}; 
-\draw (1.5,0.5) node {\large$\star$}; 
-\draw (2.5,0.5) node {\large$\star$}; 
-\draw (3.5,0.5) node {\large$\star$};
-\draw (0.5,1.5) node {\large$\star$}; 
-\draw (2.5,1.5) node {\large$\star$}; 
-\draw (0.5,3.5) node {\large$\star$}; 
-\draw (1.5,2.5) node {\large$\star$}; 
-\end{tikzpicture}}
-\end{tabular}
-\end{center}
+% \draw (0.5,0.5) node {\large$\star$}; 
+% \draw (1.5,0.5) node {\large$\star$}; 
+% \draw (2.5,0.5) node {\large$\star$}; 
+% \draw (3.5,0.5) node {\large$\star$};
+% \draw (0.5,1.5) node {\large$\star$}; 
+% \draw (2.5,1.5) node {\large$\star$}; 
+% \draw (0.5,3.5) node {\large$\star$}; 
+% \draw (1.5,2.5) node {\large$\star$}; 
+% \end{tikzpicture}}
+% \end{tabular}
+% \end{center}
 
 
-\mbox{}\\[-20mm]\mbox{}
+% \mbox{}\\[-20mm]\mbox{}
 
-\begin{center}
-\begin{tikzpicture}[>=stealth',very thick,auto,
-                             every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
-\node[state,initial]  (q_02)  {$q_{0, 2}$};
-\node[state] (q_13) [right=of q_02] {$q_{1, 3}$};
-\node[state, accepting] (q_4) [right=of q_13] {$q_{4\phantom{,0}}$};
-\path[->] (q_02) edge [bend left] node [above]  {\alert{$a$}} (q_13);
-\path[->] (q_13) edge [bend left] node [below]  {\alert{$b$}} (q_02);
-\path[->] (q_02) edge [loop below] node  {\alert{$b$}} ();
-\path[->] (q_13) edge node [above]  {\alert{$a$}} (q_4);
-\path[->] (q_4) edge [loop above] node  {\alert{$a, b$}} ();
-\end{tikzpicture}\\
-minimal automaton
-\end{center}
+% \begin{center}
+% \begin{tikzpicture}[>=stealth',very thick,auto,
+%                              every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
+% \node[state,initial]  (q_02)  {$q_{0, 2}$};
+% \node[state] (q_13) [right=of q_02] {$q_{1, 3}$};
+% \node[state, accepting] (q_4) [right=of q_13] {$q_{4\phantom{,0}}$};
+% \path[->] (q_02) edge [bend left] node [above]  {\alert{$a$}} (q_13);
+% \path[->] (q_13) edge [bend left] node [below]  {\alert{$b$}} (q_02);
+% \path[->] (q_02) edge [loop below] node  {\alert{$b$}} ();
+% \path[->] (q_13) edge node [above]  {\alert{$a$}} (q_4);
+% \path[->] (q_4) edge [loop above] node  {\alert{$a, b$}} ();
+% \end{tikzpicture}\\
+% minimal automaton
+% \end{center}
 
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+% \end{frame}
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
@@ -319,18 +319,18 @@
 \frametitle{Survey: Thanks!}
 \small
 
-\begin{itemize}
-\item {\bf My Voice} ``lecturer speaks in a low voice and 
-  is hard to hear him'' ``please use mic'' ``please use mic 
-  \& lecture recording''
-\item {\bf Pace} ``faster pace'' ``a bit quick for me 
-personally''
-\item {\bf Recording} ``please use recording class''
-\item {\bf Module Name} ``misleading''
-\item {\bf Examples} ``more examples''
-\item {\bf Assessment} ``really appreciate extension of 
-  first coursework'' 
-\end{itemize}
+% \begin{itemize}
+% \item {\bf My Voice} ``lecturer speaks in a low voice and 
+%   is hard to hear him'' ``please use mic'' ``please use mic 
+%   \& lecture recording''
+% \item {\bf Pace} ``faster pace'' ``a bit quick for me 
+% personally''
+% \item {\bf Recording} ``please use recording class''
+% \item {\bf Module Name} ``misleading''
+% \item {\bf Examples} ``more examples''
+% \item {\bf Assessment} ``really appreciate extension of 
+%   first coursework'' 
+% \end{itemize}
   
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   




