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updated
authorcu
Tue, 17 Oct 2017 13:49:45 +0100
changeset 520 2849c305b12d
parent 519 955d5b3b0619
child 521 95af9beb4b7f
updated
handouts/ho04.pdf file | annotate | diff | comparison | revisions
handouts/ho04.tex file | annotate | diff | comparison | revisions
progs/app02.scala file | annotate | diff | comparison | revisions
progs/app04.scala file | annotate | diff | comparison | revisions
progs/app61.scala file | annotate | diff | comparison | revisions
progs/token.scala file | annotate | diff | comparison | revisions
slides/slides04.pdf file | annotate | diff | comparison | revisions
slides/slides04.tex file | annotate | diff | comparison | revisions 
Binary file handouts/ho04.pdf has changed
--- a/handouts/ho04.tex	Sun Oct 15 20:47:14 2017 +0100
+++ b/handouts/ho04.tex	Tue Oct 17 13:49:45 2017 +0100
@@ -5,7 +5,7 @@
 
 
 \begin{document}
-\fnote{\copyright{} Christian Urban, King's College London, 2014, 2015, 2016}
+\fnote{\copyright{} Christian Urban, King's College London, 2014, 2015, 2016, 2017}
 
 \section*{Handout 4 (Sulzmann \& Lu Algorithm)}
 
@@ -28,7 +28,7 @@
 mathematical proof that their algorithm is really correct---the proof 
 Sulzmann \& Lu had originally given contained major flaws. Such correctness
 proofs are important: Kuklewicz maintains a unit-test library
-for the kind of algorithma we are interested in here and he showed 
+for the kind of algorithms we are interested in here and he showed 
 that many implementations in the ``wild'' are buggy, that is not
 satisfy his unit tests:
 
@@ -81,8 +81,8 @@
 corresponding to the two alternatives. Note that $r^*$ is
 associated with a list of values, one for each copy of $r$
 that was needed to match the string. This means we might also
-return the empty list $Stars []$, if no copy was needed in case
-of $r^*$. For sequence, there is exactly one value, composed 
+return the empty list $Stars []$, if no copy was needed
+for $r^*$. For sequence, there is exactly one value, composed 
 of two component values ($v_1$ and $v_2$).
 
 My implementation of regular expressions and values in Scala is
@@ -381,7 +381,7 @@
 $r_2$ or $r_{2s}$. Unfortunately, this is still not the right
 value in general because there might be some simplifications
 that happened inside $r_2$ and for which the simplification
-function retuned also a rectification function $f_{2s}$. So in
+function returned also a rectification function $f_{2s}$. So in
 fact we need to apply this one too which gives
 
 \begin{center}
@@ -587,7 +587,7 @@
    {\ifodd\value{lstnumber}\color{capri!3}\fi}]{../progs/app61.scala}
 
 \caption{The Scala code for the simplification function. The
-first part defines some auxillary functions for the rectification.
+first part defines some auxiliary functions for the rectification.
 The second part give the simplification function.
 \label{simprect}}
 \end{figure}
@@ -607,7 +607,7 @@
 
 \noindent This corresponds to the $matches$ function we have
 seen in earlier lectures. In the first clause we are given an
-empty string, $[]$, and need to test wether the regular
+empty string, $[]$, and need to test whether the regular
 expression is $nullable$. If yes, we can proceed normally and
 just return the value calculated by $\textit{mkeps}$. The second clause
 is for strings where the first character is $c$, say, and the
--- a/progs/app02.scala	Sun Oct 15 20:47:14 2017 +0100
+++ b/progs/app02.scala	Tue Oct 17 13:49:45 2017 +0100
@@ -1,7 +1,7 @@
 abstract class Val
 case object Empty extends Val
 case class Chr(c: Char) extends Val
-case class Seq(v1: Val, v2: Val) extends Val
+case class Sequ(v1: Val, v2: Val) extends Val
 case class Left(v: Val) extends Val
 case class Right(v: Val) extends Val
 case class Stars(vs: List[Val]) extends Val
--- a/progs/app04.scala	Sun Oct 15 20:47:14 2017 +0100
+++ b/progs/app04.scala	Tue Oct 17 13:49:45 2017 +0100
@@ -1,7 +1,7 @@
 abstract class Val
 case object Empty extends Val
 case class Chr(c: Char) extends Val
-case class Seq(v1: Val, v2: Val) extends Val
+case class Sequ(v1: Val, v2: Val) extends Val
 case class Left(v: Val) extends Val
 case class Right(v: Val) extends Val
 case class Stars(vs: List[Val]) extends Val
--- a/progs/app61.scala	Sun Oct 15 20:47:14 2017 +0100
+++ b/progs/app61.scala	Tue Oct 17 13:49:45 2017 +0100
@@ -6,12 +6,12 @@
   case Left(v) => Left(f1(v))
 }
 def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
-  case Seq(v1, v2) => Seq(f1(v1), f2(v2))
+  case Sequ(v1, v2) => Sequ(f1(v1), f2(v2))
 }
 def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = 
-  (v:Val) => Seq(f1(Empty), f2(v))
+  (v:Val) => Sequ(f1(Empty), f2(v))
 def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = 
-  (v:Val) => Seq(f1(v), f2(Empty))
+  (v:Val) => Sequ(f1(v), f2(Empty))
 def F_ERROR(v: Val): Val = throw new Exception("error")
 
 // simplification of regular expressions returning also a
--- a/progs/token.scala	Sun Oct 15 20:47:14 2017 +0100
+++ b/progs/token.scala	Tue Oct 17 13:49:45 2017 +0100
@@ -13,7 +13,7 @@
 abstract class Val
 case object Empty extends Val
 case class Chr(c: Char) extends Val
-case class Seq(v1: Val, v2: Val) extends Val
+case class Sequ(v1: Val, v2: Val) extends Val
 case class Left(v: Val) extends Val
 case class Right(v: Val) extends Val
 case class Stars(vs: List[Val]) extends Val
@@ -79,7 +79,7 @@
   case Chr(c) => c.toString
   case Left(v) => flatten(v)
   case Right(v) => flatten(v)
-  case Seq(v1, v2) => flatten(v1) + flatten(v2)
+  case Sequ(v1, v2) => flatten(v1) + flatten(v2)
   case Stars(vs) => vs.map(flatten).mkString
   case Rec(_, v) => flatten(v)
 }
@@ -90,7 +90,7 @@
   case Chr(c) => Nil
   case Left(v) => env(v)
   case Right(v) => env(v)
-  case Seq(v1, v2) => env(v1) ::: env(v2)
+  case Sequ(v1, v2) => env(v1) ::: env(v2)
   case Stars(vs) => vs.flatMap(env)
   case Rec(x, v) => (x, flatten(v))::env(v)
 }
@@ -100,17 +100,17 @@
   case ONE => Empty
   case ALT(r1, r2) => 
     if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))
-  case SEQ(r1, r2) => Seq(mkeps(r1), mkeps(r2))
+  case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))
   case STAR(r) => Stars(Nil)
   case RECD(x, r) => Rec(x, mkeps(r))
 }
 
 
 def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {
-  case (STAR(r), Seq(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
-  case (SEQ(r1, r2), Seq(v1, v2)) => Seq(inj(r1, c, v1), v2)
-  case (SEQ(r1, r2), Left(Seq(v1, v2))) => Seq(inj(r1, c, v1), v2)
-  case (SEQ(r1, r2), Right(v2)) => Seq(mkeps(r1), inj(r2, c, v2))
+  case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
+  case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2)
+  case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2)
+  case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2))
   case (ALT(r1, r2), Left(v1)) => Left(inj(r1, c, v1))
   case (ALT(r1, r2), Right(v2)) => Right(inj(r2, c, v2))
   case (CHAR(d), Empty) => Chr(c) 
@@ -140,12 +140,12 @@
   case Left(v) => Left(f1(v))
 }
 def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
-  case Seq(v1, v2) => Seq(f1(v1), f2(v2))
+  case Sequ(v1, v2) => Sequ(f1(v1), f2(v2))
 }
 def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = 
-  (v:Val) => Seq(f1(Empty), f2(v))
+  (v:Val) => Sequ(f1(Empty), f2(v))
 def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = 
-  (v:Val) => Seq(f1(v), f2(Empty))
+  (v:Val) => Sequ(f1(v), f2(Empty))
 def F_RECD(f: Val => Val) = (v:Val) => v match {
   case Rec(x, v) => Rec(x, f(v))
 }
Binary file slides/slides04.pdf has changed
--- 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}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
afl-material