
diff -r 070f543e2560 -r d94209ad2880 pres/document/fig_seq.tex
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/pres/document/fig_seq.tex	Thu Feb 03 12:00:06 2011 +0000
@@ -0,0 +1,102 @@
+\begin{figure}[h!]
+\centering
+
+\subfigure[First possible way to split $x@z$]{\label{seq_first_split}
+\scalebox{0.7}{
+\begin{tikzpicture}
+    \node[draw,minimum height=3.8ex] (xa) { $\hspace{4em}xa\hspace{4em}$ };
+    \node[draw,minimum height=3.8ex, right=-0.03em of xa] (xxa) { $\hspace{0.5em}x - xa\hspace{0.5em}$ };
+    \node[draw,minimum height=3.8ex, right=-0.03em of xxa] (z) { $\hspace{21em}$ };
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           (xa.north west) -- ($(xxa.north east)+(0em,0em)$)
+               node[midway, above=0.5em]{$x$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           (z.north west) -- ($(z.north east)+(0em,0em)$)
+               node[midway, above=0.5em]{$z$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(xa.north west)+(0em,3ex)$) -- ($(z.north east)+(0em,3ex)$)
+               node[midway, above=0.8em]{$x @ z \in L_1 ;; L_2$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(z.south east)+(0em,0ex)$) -- ($(xxa.south west)+(0em,0ex)$)
+               node[midway, below=0.5em]{$(x - xa) @ z \in L_2$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(xa.south east)+(0em,0ex)$) -- ($(xa.south west)+(0em,0ex)$)
+               node[midway, below=0.5em]{$xa \in L_1$};
+\end{tikzpicture}}}
+
+\subfigure[Transferred structure corresponding to the first way of splitting]{\label{seq_trans_first_split}
+\scalebox{0.7}{
+\begin{tikzpicture}
+    \node[draw,minimum height=3.8ex] (xa) { $\hspace{4em}ya\hspace{4em}$ };
+    \node[draw,minimum height=3.8ex, right=-0.03em of xa] (xxa) { $\hspace{0.5em}y - ya\hspace{0.5em}$ };
+    \node[draw,minimum height=3.8ex, right=-0.03em of xxa] (z) { $\hspace{21em}$ };
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           (xa.north west) -- ($(xxa.north east)+(0em,0em)$)
+               node[midway, above=0.5em]{$y$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           (z.north west) -- ($(z.north east)+(0em,0em)$)
+               node[midway, above=0.5em]{$z$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(xa.north west)+(0em,3ex)$) -- ($(z.north east)+(0em,3ex)$)
+               node[midway, above=0.8em]{$y @ z \in L_1 ;; L_2$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(z.south east)+(0em,0ex)$) -- ($(xxa.south west)+(0em,0ex)$)
+               node[midway, below=0.5em]{$(y - ya) @ z \in L_2$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(xa.south east)+(0em,0ex)$) -- ($(xa.south west)+(0em,0ex)$)
+               node[midway, below=0.5em]{$ya \in L_1$};
+\end{tikzpicture}}}
+
+\subfigure[The second possible way to split $x@z$]{\label{seq_snd_split}
+\scalebox{0.7}{
+\begin{tikzpicture}
+    \node[draw,minimum height=3.8ex] (x) { $\hspace{6.5em}x\hspace{6.5em}$ };
+    \node[draw,minimum height=3.8ex, right=-0.03em of x] (za) { $\hspace{2em}za\hspace{2em}$ };
+    \node[draw,minimum height=3.8ex, right=-0.03em of za] (zza) { $\hspace{6.1em}z - za\hspace{6.1em}$  };
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(za.north west)+(0em,0ex)$) -- ($(zza.north east)+(0em,0ex)$)
+               node[midway, above=0.8em]{$z$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(x.north west)+(0em,3ex)$) -- ($(zza.north east)+(0em,3ex)$)
+               node[midway, above=0.8em]{$x @ z \in L_1 ;; L_2$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(za.south east)+(0em,0ex)$) -- ($(x.south west)+(0em,0ex)$)
+               node[midway, below=0.5em]{$x @ za \in L_1$};
+\end{tikzpicture}}}
+
+
+\subfigure[Transferred structure corresponding to the second way of splitting]{\label{seq_trans_snd_split}
+\scalebox{0.7}{
+\begin{tikzpicture}
+    \node[draw,minimum height=3.8ex] (x) { $\hspace{6.5em}y\hspace{6.5em}$ };
+    \node[draw,minimum height=3.8ex, right=-0.03em of x] (za) { $\hspace{2em}za\hspace{2em}$ };
+    \node[draw,minimum height=3.8ex, right=-0.03em of za] (zza) { $\hspace{6.1em}z - za\hspace{6.1em}$  };
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(za.north west)+(0em,0ex)$) -- ($(zza.north east)+(0em,0ex)$)
+               node[midway, above=0.8em]{$z$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(x.north west)+(0em,3ex)$) -- ($(zza.north east)+(0em,3ex)$)
+               node[midway, above=0.8em]{$y @ z \in L_1 ;; L_2$};
+
+    \draw[decoration={brace,transform={yscale=3}},decorate]
+           ($(za.south east)+(0em,0ex)$) -- ($(x.south west)+(0em,0ex)$)
+               node[midway, below=0.5em]{$y @ za \in L_1$};
+\end{tikzpicture}}}
+
+\caption{The case for $SEQ$}
+\end{figure}




