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\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
$S_1$ & 0 & 1 & 1 & $\ldots$ & $correct$ \\
$S_2$ & 1 & 0 & 0 & $\ldots$ & $correct$ \\
$S_3$ & 1 & 1 & 0 & $\ldots$ & $incorrect$ \\
$\vdotswithin{S_4}$ & & $\vdotswithin{1}$ & & & $\vdotswithin{correct}$ \\
\end{tabular}
\end{column}
\end{columns}
\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}{0.42\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}
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{\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):
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):
%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}
%\end{Verbatim}
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