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diff --git a/aied2018/presentation/rules.tex b/aied2018/presentation/rules.tex
index f2a31c7..b974530 100644
--- a/aied2018/presentation/rules.tex
+++ b/aied2018/presentation/rules.tex
@@ -1,8 +1,14 @@
 \textbf{The dataset}
 
 \begin{columns}
+\begin{column}{0.50\textwidth}
+	\begin{itemize}
+		\item $S_i$: submitted programs
+		\item $P_i$: patterns (binary features)
+		\item each submission is classified either as $correct$ or $incorrect$ based on test cases
+	\end{itemize}
+\end{column}
 \begin{column}{0.40\textwidth}
-
 \begin{tabular}{l|rrrr|l}
 	& $P_1$ & $P_2$ & $P_3$ & $\ldots$ & class \\
 	\hline
@@ -12,98 +18,121 @@ $S_3$ &	1 & 1 & 0 & $\ldots$ & $incorrect$ \\
 $\vdotswithin{S_4}$ & & $\vdotswithin{1}$ & & & $\vdotswithin{correct}$ \\
 \end{tabular}
 \end{column}
-\begin{column}{0.60\textwidth}
-	\begin{itemize}
-		\item Each submission ($S_1, S_2, S_3, \ldots$) becomes a learning instance.
-		\item Each constructed pattern ($P_1, P_2, P_3, \ldots$) is a binary feature.
-		\item Based on test results each submission is classified either as $correct$ or $incorrect$
-	\end{itemize}
-\end{column}
 \end{columns}
-\vspace{2cm}
 
+\vspace{1cm}
+
+\textbf{Characterizing errors and solutions}
+\vspace{0.5cm}
 
+Induce rules to predict whether a program is correct (\emph{p-rules}) or not (\emph{n-rules}) based on patterns that appear in it.
+
+\vspace{1cm}
 \begin{columns}
-	\begin{column}{0.01\textwidth}
-	\end{column}
-	\begin{column}{0.59\textwidth}
-		\textbf{Characterizing typical approaches and errors with rule learning}
-		\begin{itemize}
-			\item \emph{n-rules} describe buggy patterns: \\IF $condition$ THEN $incorrect$. 
-			\item \emph{p-rules} describe necessary patterns for programs to be correct: \\IF $condition$ THEN $correct$.
-		\end{itemize}
-	    \vspace{0.5cm}
-		\textbf{Example: Greatest Absolutist}
-		\begin{itemize}
-			\item 155 submissions (57 correct, 98 incorrect)
-			\item 8298 patterns, 15 n-rules and 6 p-rules
-		\end{itemize}		
-		\underline{\smash{A solution:}}
-		\begin{Verbatim}
+	\begin{column}{0.42\textwidth}
+        \textbf{\emph{n-rules}} describe errors: \\IF $P_1 \land \ldots \land P_k$ THEN $incorrect$
+        \end{column}
+	\begin{column}{0.50\textwidth}
+        \textbf{\emph{p-rules}} describe alternative solutions: \\IF $P_1 \land \ldots \land P_k$ THEN $correct$
+        \end{column}
+\end{columns}
+
+\vspace{1.5cm}
+
+\begin{columns}[T]
+        \begin{column}{0.58\textwidth}
+\textbf{Example: Greatest Absolutist}
+
+\vspace{0.5cm}
+Find element with the largest absolue value.
+
+\vspace{0.5cm}
+\begin{Verbatim}
 \textbf{def} max_abs(l):
   vmax = l[0]
   \textbf{for} v \textbf{in} l:
     \textbf{if} abs(v) > abs(vmax):
       vmax = v
   \textbf{return} vmax
-		\end{Verbatim}
-		\vspace{0.5cm}
-		\underline{\smash{Two sample learned n-rules:}}
-				\begin{itemize}
-			\item \textsf{P64 ⇒ incorrect } (covers 22)
-			\item \textsf{P2 ∧ P70 ⇒ incorrect} (covers 17)
-		\end{itemize}
-
-	\end{column}
-	\begin{column}{0.40\textwidth}
-		\fbox{
-		\begin{minipage}[t]{0.94\textwidth}
-		\vspace{0.5cm}
-		\textbf{How useful are patterns?}
-		\begin{itemize}
-			\item Compare accuracies of Random Forest and Majority Classifier.
-			\item Three types of exercises (basic, loops, functions)
-		\end{itemize}
-		\vspace{0.5cm}
-		\begin{center}
-		\begin{tabular}{l|rr}
-		\textbf{Problem} &  Maj & RF \\
-		\hline
-		\textsf{F2C}&  0.579 & 0.933  \\
-		\textsf{ballistics}&  0.761 & 0.802  \\
-		\textsf{average}&  0.614 & 0.830  \\
-		\hline
-		\textsf{buy\_five}&  0.613 & 0.828  \\
-		\textsf{competition}&  0.703 & 0.847  \\
-		\textsf{top\_shop}&  0.721 & 0.758  \\
-		\textsf{minimax}&  0.650 & 0.644  \\
-		\textsf{ch\_account}&  0.521 & 0.744 \\
-		\textsf{con\_anon}&  0.688 & 0.800  \\
-		\hline
-		\textsf{greatest}&  0.585 & 0.859 \\
-		\textsf{greatest\_abs}&  0.632 & 0.845  \\
-		\textsf{greatest\_neg}&  0.636 & 0.815  \\
-		\hline
-		Average & 0.642 & 0.809 \\
-		\end{tabular}
-		\end{center}
-		\end{minipage}}
-	\end{column}
-\end{columns}
-\vspace{1.5cm}
-\underline{\smash{Vizualizations of rules / patterns}}
+\end{Verbatim}
+
+\vspace{0.5cm}
+We collected 155 submissions for this problem. Using extracted patterns our approach induced 15~n-rules and 6~p-rules.
+
+\vspace{1cm}
+\underline{\smash{Example n-rules}}
+
+\vspace{0.5cm}
 \begin{itemize}
-	\item \textsf{P64} (blue left) matches functions returning variable compared in the \textsf{if} clause.
-	\item \textsf{P2} (red right) matches functions that return the variable used in an assignment statement within a for-if block;	\textsf{P70} (blue) matches the call to \textsf{abs} in an assignment statement nested within a for loop and an if clause.
+    \item \textsf{\green{$P_G$} ⇒ incorrect } (covers 22)
+    \item \textsf{$\red{P_R} ∧ \blue{P_B}$ ⇒ incorrect} (covers 17)
 \end{itemize}
+
+\end{column}
+
+\begin{column}{0.35\textwidth}
+        \textbf{Results}
+
+        \vspace{0.5cm}
+
+        \fbox{
+        \begin{minipage}[t]{0.99\textwidth}
+        \begin{center}
+        \begin{tabular}{l|rr}
+        \textbf{Problem} &  Maj & RF \\
+        \hline
+        \textsf{F2C}&  0.579 & 0.933  \\
+        \textsf{ballistics}&  0.761 & 0.802  \\
+        \textsf{average}&  0.614 & 0.830  \\
+        \hline
+        \textsf{buy\_five}&  0.613 & 0.828  \\
+        \textsf{competition}&  0.703 & 0.847  \\
+        \textsf{top\_shop}&  0.721 & 0.758  \\
+        \textsf{minimax}&  0.650 & 0.644  \\
+        \textsf{ch\_account}&  0.521 & 0.744 \\
+        \textsf{con\_anon}&  0.688 & 0.800  \\
+        \hline
+        \textsf{greatest}&  0.585 & 0.859 \\
+        \textsf{greatest\_abs}&  0.632 & 0.845  \\
+        \textsf{greatest\_neg}&  0.636 & 0.815  \\
+        \hline
+        Average & 0.642 & 0.809 \\
+        \end{tabular}
+        \end{center}
+        \end{minipage}}
+\end{column}
+\end{columns}
+
+\vspace{2cm}
+\underline{\smash{Vizualizing rules / patterns}}
+
+\begin{columns}
+\begin{column}{0.4\textwidth}
 \begin{Verbatim}
-\textbf{def} max_abs(l):         \textbf{def} max_abs(l):
-  vmax = 0                vmax = None 
-  \textbf{for} i \textbf{in} range(len(l)): \textbf{for} v \textbf{in} l:
-    \textbf{if} \blue{vmax} < abs(l[i]):     \textbf{if} vmax==None or vmax<v:
-      vmax = l[i]               \red{vmax} = \blue{abs}(v)
-  \textbf{return} \blue{vmax}             \textbf{return} \red{vmax}
+\textbf{def} max_abs(l):
+  vmax = 0
+  \textbf{for} i \textbf{in} range(len(l)):
+    \textbf{if} \textbf{\green{vmax}} < abs(l[i]):
+      vmax = l[i]
+  \textbf{return} \textbf{\green{vmax}}
 \end{Verbatim}
+\end{column}
+\begin{column}{0.55\textwidth}
+\begin{Verbatim}
+\textbf{def} max_abs(l):
+  vmax = None
+  \textbf{for} v \textbf{in} l:
+    \textbf{if} vmax==None \textbf{or} vmax<v:
+      \textbf{\red{vmax}} = \textbf{\blue{abs}}(v)
+  \textbf{return} \textbf{\red{vmax}}
+\end{Verbatim}
+\end{column}
+\end{columns}
+
+\vspace{1.5cm}
+\textbf{Evaluation.}
+We evaluated this approach on exercises covering introduction to Python, loops and functions,
+by comparing the classification accuracy of a random-forest classifier based on patterns to the majority classifier. 
 
 %\begin{Verbatim}
 %\textbf{def} max_abs(l):         \textbf{def} max_abs(l):