add cyk

Section04-Phrasal-and-Syntactic-Models/section04.tex

@@ -3754,6 +3754,70 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
 \begin{frame}{CYK算法}
 % 看NiuTrans Manual
 \begin{itemize}
+\item CYK算法通过遍历不同\alert{span}来判断字符串是否符合文法
+	\begin{itemize}
+	\item 输入：源语串\textbf{s =} $s_1 ... s_J$，以及上下文无关文法$G$
+	\item 输出：判断字符串是否符合上下文无关文法
+	\end{itemize}
+%\vspace{-0.5em}
+\begin{center}
+\begin{tikzpicture}
+\tikzstyle{alignmentnode} = [rectangle,fill=blue!30,minimum size=0.45em,text=white,inner sep=0.1pt]
+\tikzstyle{selectnode} = [rectangle,fill=green!20,minimum height=1.5em,minimum width=1.5em,inner sep=1.2pt]
+\tikzstyle{srcnode} = [anchor=south west]
+\begin{scope}[scale=0.85]
+\node[srcnode] (c1) at (0,0) {\small{\textbf{Function} CKY-Algorithm($s,G$)}};
+\node[srcnode,anchor=north west] (c21) at ([xshift=2em,yshift=0.4em]c1.south west) {\small{\textbf{foreach} ($j_1, j_2$): 1$ \leq j_1 \leq J$ and 1$ \leq j_2 \leq J$}};
+\node[srcnode,anchor=north west] (c22) at ([xshift=2em,yshift=0.4em]c21.south west) {\small{Initialize $cell[j_1,j_2 ]$}};
+\node[srcnode,anchor=north west] (c3) at ([xshift=-2em,yshift=0.4em]c22.south west) {\small{\textbf{for} $j_1$ = 1 to $J$}};
+\node[srcnode,anchor=west] (c31) at ([xshift=5em]c3.east) {\small{// beginning of span}};
+\node[srcnode,anchor=north west] (c4) at ([xshift=2em,yshift=0.4em]c3.south west) {\small{\textbf{for} $j_2$ = $j_1$ to $J$}};
+\node[srcnode,anchor=north west] (c41) at ([yshift=0.4em]c31.south west) {\small{// ending of span}};
+\node[srcnode,anchor=north west] (c5) at ([xshift=2em,yshift=0.4em]c4.south west) {\small{\textbf{for} $k$ = $j_1$ to $j_2$}};
+\node[srcnode,anchor=north west] (c51) at ([yshift=0.4em]c41.south west) {\small{// partition of span}};
+\node[srcnode,anchor=north west] (c6) at ([xshift=2em,yshift=0.4em]c5.south west) {\small{$hypos$ = Compose($cell[j_1, k], cell[k, j_2]$)}};
+\node[srcnode,anchor=north west] (c7) at ([yshift=0.4em]c6.south west) {\small{$cell[j_1, j_2]$.update($hypos$)}};
+\node[srcnode,anchor=north west] (c8) at ([xshift=-6em,yshift=0.4em]c7.south west) {\small{\textbf{return} $cell[1, J]$}};
+
+
+\node[srcnode] (s1) at ([yshift=-2.5em]c8.south west) {\textbf{s:}};
+\node[srcnode] (s2) at ([xshift=1em]s1.south east) {$s_1$};
+\node[srcnode] (s3) at ([xshift=1em]s2.south east) {$s_2$};
+\node[srcnode] (s4) at ([xshift=1em]s3.south east) {$s_3$};
+\node[srcnode] (s5) at ([xshift=1em]s4.south east) {$s_4$};
+\node[srcnode] (s6) at ([xshift=1em]s5.south east) {$s_5$};
+\node[srcnode] (s7) at ([xshift=1em]s6.south east) {$s_6$};
+\node[srcnode] (s8) at ([xshift=1em]s7.south east) {$s_7$};
+
+\node[srcnode,anchor=center] (j1) at ([yshift=-1.4em]s3.south) {$j_1$};
+\node[srcnode,anchor=center] (j2) at ([yshift=-1.4em]s7.south) {$j_2$};
+
+\node[srcnode,anchor=center] (k) at ([xshift=1.5em,yshift=-1.5em]s4.south) {$k$};
+
+\draw[->,thick] ([yshift=-0.1em]j1.north)--([yshift=0.1em]s3.south);
+\draw[->,thick] ([yshift=-0.1em]j2.north)--([yshift=0.1em]s7.south);
+\draw[->,thick] ([yshift=-0.1em]k.north)--([xshift=1.5em,yshift=0.1em]s4.south);
+
+\node [rectangle,inner sep=0.3em,rounded corners=1pt,very thick,dotted,draw=ugreen] [fit = (s3) (s7)] (box1) {};
+
+\begin{pgfonlayer}{background}
+\node [rectangle,inner sep=0.2em,rounded corners=1pt,fill=blue!10!white] [fit = (c1) (c21) (c3) (c6) (c7) (c8)] (gl1) {};
+\node [rectangle,inner sep=0.3em,rounded corners=1pt,fill=green!10!white] [fit = (s3) (s4)] (box2) {};
+\node [rectangle,inner sep=0.3em,rounded corners=1pt,fill=red!10!white] [fit = (s5) (s7)] (box3) {};
+\end{pgfonlayer}
+
+\end{scope}
+
+\end{tikzpicture}
+\end{center}
+\end{itemize}
+\end{frame}
+
+%%%------------------------------------------------------------------------------------------------------------
+%%%  CYK解码
+\begin{frame}{CYK算法}
+% 看NiuTrans Manual
+\begin{itemize}
 \item 我们来看一个CYK算法的具体例子，给定一个上下无关文法以及一个单词\alert{aabbc}，来判断该单词是否属于此文法，解析流程如下
 \vspace{-0.5em}
 \begin{center}