extend flowchart

latex/splash2024/method/method.tex

@@ -14,12 +14,14 @@
 \tikzstyle{startstop} = [rectangle, rounded corners,
 minimum width=3cm,
 minimum height=1cm,
+thick,
 text centered,
 draw=black,
 fill=red!30]
 
 \tikzstyle{io} = [trapezium,
 trapezium stretches=true, % A later addition
+thick,
 trapezium left angle=70,
 trapezium right angle=110,
 minimum width=3cm,
@@ -29,80 +31,88 @@
 \tikzstyle{process} = [rectangle,
 minimum width=3.5cm,
 minimum height=1cm,
+thick,
 text centered,
-text width=3.5cm,
+text width=4cm,
 draw=black,
 fill=orange!30]
 
 \tikzstyle{decision} = [diamond,
 minimum width=3cm,
 minimum height=1cm,
+thick,
 text centered,
 draw=black,
 fill=green!30]
-\tikzstyle{arrow} = [thick,->,>=stealth]
+\tikzstyle{arrow} = [->,thick]
 \begin{document}
 
 % Document
 \begin{document}
 
 \section{Method}
 
-The syntax of most programming languages is context-free. Our proposed method is simple. We construct a context-free grammar representing the intersection between the langauge syntax and an automaton recognizing the Levenshtein edit ball up to a fixed distance. Since CFLs are closed under intersection with regular languages, this is admissible. Three outcomes are possible:
+The syntax of most programming languages is context-free. Our proposed method is simple. We construct a context-free grammar representing the intersection between the langauge syntax and an automaton recognizing the Levenshtein ball of a given radius. Since CFLs are closed under intersection with regular languages, this is admissible. Three outcomes are possible:
 
 \begin{enumerate}
   \item $\mathcal{G}_\cap$ is empty, in which case there is no repair within the given radius. In this case, we simply increase the radius and try again.
-  \item $\mathcal{G}_\cap$ is small, in which case we simply enumerate all possible repairs. This is the case for ~80\% of the Python dataset.
-  \item $\mathcal{G}_\cap$ is too large to exhaustively sample, in which case we use a PCFG to sample $\mathcal{L}(\mathcal{G})$ without replacement, then reject duplicates. This is the case for ~20\% of the Python dataset.
+  \item $\mathcal{L}(\mathcal{G}_\cap)$ is small, in which case we simply enumerate all possible repairs. Enumeration is tractable for $\sim 80\%$ of the Python dataset in $\leq 90$s.
+  \item $\mathcal{L}(\mathcal{G}_\cap)$ is too large to enumerate, so we sample from the intersection grammar $\mathcal{G}_\cap$. Sampling is necessary for $\sim20\%$ of the Python dataset.
 \end{enumerate}
 
-After sampling, we use an n-gram model to rank the samples, then return the top-k results by likelihood. We depict the flowchart below:
+When ambiguous, we use an n-gram model to rank and return the top-k results by likelihood. This procedure is depicted in the flowchart below:
 
 \begin{figure}[h!]
   \begin{center}
 \resizebox{0.6\textwidth}{!}{
 \begin{tikzpicture}[node distance=2cm]
 
-%  \node (start) [startstop] {Start};
-  \node (in1) [io] {Input};
-  \node (rin1) [io, right of=in1, xshift=3cm] {L-NFA};
-  \node (lin1) [io, left of=in1, xshift=-3cm] {[P]CFG};
+  \node (start) [startstop] {Start};
+  \node (pro1) [process, below of=start, yshift=-0.5cm] {$\mathcal{G}_\cap \leftarrow \mathcal{G}\cap\Delta(\err\sigma, d)$};
+  \node (pcfg) [io, left of=pro1, xshift=-3cm] {[P]CFG};
+  \node (lnfa) [io, right of=pro1, xshift=3cm] {L-WFA};
 
-  \node (pro1) [process, below of=in1] {$\mathcal{G}_\cap \leftarrow \mathcal{G}\cap\Delta(\err\sigma, d)$};
+  \node (code) [io, right of=start,xshift=3cm] {Code};
+  \node (synt) [io, left of=start,xshift=-3cm] {Syntax};
 
   \node (dec1) [decision, below of=pro1, yshift=-0.5cm] {$[\mathcal{G}_{\cap} = \varnothing]$};
 
-  \node (pro2b) [process, right of=dec1, xshift=3cm] {Increase radius};
+  \node (pro2b) [process, right of=dec1, xshift=3cm] {Increase radius, $d$};
 
-  \node (dec2) [decision, below of=dec1, yshift=-0.8cm] {$|\mathcal{L}(\mathcal{G}_\cap)|$};
+  \node (dec2) [decision, below of=dec1, yshift=-1cm] {$|\mathcal{L}(\mathcal{G}_\cap)|$};
 
-  \node (samp1) [process, left of=dec2, xshift=-3cm] {Denumerate $\mathcal{L}(\mathcal{G}_\cap)$};
-  \node (samp2) [process, right of=dec2, xshift=3cm] {Sample [P]CFG};
+  \node (samp1) [process, left of=dec2, xshift=-3cm] {Enumerate $\sigma' \in \mathcal{L}(\mathcal{G}_\cap)$};
+  \node (samp2) [process, right of=dec2, xshift=3cm] {Sample $\sigma' \sim P(\mathcal{G}_\cap)$};
 
-  \node (uin1) [io, below of=dec2, yshift=0.1cm] {VOMC};
-  \node (rank1) [process, below of=uin1, yshift=0.1cm] {Rerank solutions};
+  \node (rank) [process, below of=dec2, yshift=-2.5cm] {Rerank by $L_\theta(\sigma')$};
+  \node (vlmc) [io, below of=rank, yshift=-0.1cm] {VLMC};
 
 %  \node (out1) [io, below of=pro2a] {Output};
-%  \node (stop) [startstop, below of=out1] {Stop};
+  \node (stop) [startstop, above of=rank] {Done};
 
-%  \draw [arrow] (start) -- (in1);
+%  \draw [arrow] (dec0) -- node[anchor=east] {no} (pro1);
 
-  \draw [arrow] (rin1) -- (in1);
-  \draw [arrow] (lin1) -- (in1);
+  \draw [arrow] (start) -- (code);
+  \draw [arrow] (start) -- (synt);
+  \draw [arrow] (code) -- (lnfa);
+  \draw [arrow] (synt) -- (pcfg);
+  \draw [arrow] (lnfa) -- (pro1);
+  \draw [arrow] (pcfg) -- (pro1);
 
-  \draw [arrow] (in1) -- (pro1);
+%  \draw [arrow] (in1) -- (pro1);
   \draw [arrow] (pro1) -- (dec1);
   \draw [arrow] (dec1) -- node[anchor=south] {yes} (pro2b);
   \draw [arrow] (dec1) -- node[anchor=east] {no} (dec2);
-  \draw [arrow] (pro2b) -- (rin1);
+  \draw [arrow] (pro2b) -- (lnfa);
   \draw [arrow] (dec2) -- node[anchor=south] {small} (samp1);
   \draw [arrow] (dec2) -- node[anchor=south] {large} (samp2);
 
-  \draw [arrow] (uin1) -- (rank1);
-  \draw [arrow] (samp1) |- (rank1);
-  \draw [arrow] (samp2) |- (rank1);
+  \draw [arrow] (vlmc) -- (rank);
+  \draw [arrow] (samp1) |- (rank);
+  \draw [arrow] (samp2) |- (rank);
 %  \draw [arrow] (pro2a) -- (out1);
-%  \draw [arrow] (out1) -- (stop);
+  \draw [arrow] (rank) -- (stop);
+  \draw [arrow] (dec2) -- node[anchor=east] {1} (stop);
 
 \end{tikzpicture}
 }