%.pdf : %.tex
lualatex -shell-escape $< </dev/null > $<.build_log
-all : mark_enum.pdf pe.pdf pe2.pdf trees.pdf tnfa.pdf gor1.pdf
+all : mark_enum.pdf pe.pdf pe2.pdf pe3.pdf trees.pdf tnfa.pdf gor1.pdf
clean:
rm *.log *.build_log *.aux *.pdf *.pag
\begin{tikzpicture}[>=stealth, ->, auto, node distance=0.2in]
-\tikzstyle{every node}=[draw=none]
+\tikzstyle{every node}=[draw=none, shape=rectangle, , outer sep = 0in];
% $(\epsilon|a^{0,\infty})(a|\epsilon)^{0,\infty}$
\begin{scope}[xshift=0.5in, yshift=0in]
- \node (a) {\small{
+ \node (a) {{
$\begin{aligned}
& mark (((\epsilon|a^{0,\infty})(a|\epsilon)^{0,3} ))) = \big[ \\
& \quad mark ( (\epsilon|a^{0,\infty})(a|\epsilon)^{0,3} ) ) = \big[ \\
& \big] = (1,1,
(1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
& \quad\quad\quad \cdot (1,0,(1,1,(0,0,a) \mid (0,0,\epsilon))^{0,3})
- )
+ ) \\
+%
+% & \IRE ((\epsilon|a^{0,\infty})(a|\epsilon)^{0,3} )) = \\
+% & \quad\quad\quad = (1,1, (2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
+% & \quad\quad\quad\quad\quad\quad \cdot (3,0,(4,3,(0,0,a) \mid (0,0,\epsilon))^{0,3}))
\end{aligned}$
}};
\end{scope}
\begin{scope}[xshift=4in, yshift=0in]
- \node (a) {\small{
+ \node (a) {{
$\begin{aligned}
& enum (1,1,(1,1,
(1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
(2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
& \quad\quad\quad\quad\quad \cdot (3,0,(4,3,(0,0,a) \mid (0,0,\epsilon))^{0,3})
)) \\
- \\
- \\
- & \IRE ((\epsilon|a^{0,\infty})(a|\epsilon)^{0,3} )) = \\
- & \quad\quad\quad = (1,1, (2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
- & \quad\quad\quad\quad\quad\quad \cdot (3,0,(4,3,(0,0,a) \mid (0,0,\epsilon))^{0,3}))
- \\
- \\
+ \\ \\ \\ \\ \\ \\ \\
\end{aligned}$
}};
\end{scope}
-\begin{scope}[xshift=2.5in, yshift=-2.4in]
+\begin{scope}[xshift=2.5in, yshift=-2.9in]
+ \node (c) {{
+ $\begin{aligned}
+ & \IRE ((\epsilon|a^{0,\infty})(a|\epsilon)^{0,3} ))
+ = (1,1, (2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))
+ \cdot (3,0,(4,3,(0,0,a) \mid (0,0,\epsilon))^{0,3}))
+ \end{aligned}$
+ }};
+\end{scope}
+
+\begin{scope}[xshift=4in, yshift=-1.35in]
\graph [tree layout, grow=down, fresh nodes] {
"${(1, 1, \cdot)}_{\Lambda}$" -- {
"${(2, 2, |)}_{1}$" -- {
- "${(0, 0, \epsilon)}_{1.1}$"[draw=none],
- "${(0, 0, \{0,\infty\})}_{1.2}$"[draw=none] -- {
- "${(0, 0, a)}_{1.2.1}$"[draw=none]
+ "${(0, 0, \epsilon)}_{1.1}$",
+ "${(0, 0, \{0,\infty\})}_{1.2}$" -- {
+ "${(0, 0, a)}_{1.2.1}$"
}
},
"${(3, 0, \{0,3\})}_{2}$" -- {
"${(4, 3, |)}_{2.1}$" -- {
- "${(0, 0, a)}_{2.1.1}$"[draw=none],
- "${(0, 0, \epsilon)}_{2.1.2}$"[draw=none]
+ "${(0, 0, a)}_{2.1.1}$",
+ "${(0, 0, \epsilon)}_{2.1.2}$"
}
}
}
};
\end{scope}
-\begin{scope}[xshift=0.2in, yshift=-4in]
- \node[xshift=-0.3in, draw=none] {$s:$};
+\newcommand\xsp[1]{\hphantom{\hspace{#1em}\hspace{-0.2em}}}
+
+\begin{scope}[xshift=0in, yshift=-3.3in, sibling distance=0.6in]
+ \node[xshift=-0.2in, draw=none] {$s:$};
\graph [tree layout, grow=down, fresh nodes] {
- "${T}^{1}_{\Lambda}$" -- {
- "${T}^{2}_{1}$" -- {
- "${\varnothing}^{0}_{1.1}$"[draw=none],
- "${T}^{0}_{1.2}$"[draw=none] -- {
- "${a}^{0}_{1.2.1}$"[draw=none]
+ a1/"${T}^{1}_{\Lambda}$" -- {
+ a11/"${T}^{2}_{1}$" -- {
+ a111/"${\varnothing}^{0}_{1.1}$",
+ a112/"${T}^{0}_{1.2}$" -- {
+ a1121/"${a}^{0}_{1.2.1}$"
}
},
- "${T}^{3}_{2}$" -- {
- "${\varnothing}^{4}_{2.1}$"
+ a12/"${T}^{3}_{2}$" -- {
+ a121/"${\varnothing}^{4}_{2.1}$"
}
}
};
+ \node at (a1) {\xsp{2.5}\footnotesize{$\#1$}};
+ \node at (a11) {\xsp{2.5}\footnotesize{$\#1$}};
+ \node at (a111) {\xsp{3.0}\footnotesize{$\#\infty$}};
+ \node at (a112) {\xsp{3.0}\footnotesize{$\#\infty$}};
+ \node at (a1121) {\xsp{3.5}\footnotesize{$\#\infty$}};
+ \node at (a12) {\xsp{2.5}\footnotesize{$\#0$}};
+ \node at (a121) {\xsp{3.0}\footnotesize{$\#\!-\!\!1$}};
+
\node[yshift=-1.5in, draw=none]
{\small{${T}^{1} \big(
{T}^{2} \big(
\big)$}};
\end{scope}
-\begin{scope}[xshift=2.1in, yshift=-4in]
- \node[xshift=-0.3in, draw=none] {$t:$};
+\begin{scope}[xshift=1.9in, yshift=-3.3in, sibling distance=0.6in]
+ \node[xshift=-0.2in, draw=none] {$t:$};
\graph [tree layout, grow=down, fresh nodes] {
- "${T}^{1}_{\Lambda}$" -- {
- "${T}^{2}_{1}$" -- {
- "${\varnothing}^{0}_{1.1}$"[draw=none],
- "${T}^{0}_{1.2}$"[draw=none] -- {
- "${\varnothing}^{0}_{1.2.1}$"[draw=none]
+ a1/"${T}^{1}_{\Lambda}$" -- {
+ a11/"${T}^{2}_{1}$" -- {
+ a111/"${\varnothing}^{0}_{1.1}$",
+ a112/"${T}^{0}_{1.2}$" -- {
+ a1121/"${\varnothing}^{0}_{1.2.1}$"
}
},
- "${T}^{3}_{2}$" -- {
- "${T}^{4}_{2.1}$" -- {
- "${a}^{0}_{2.1.1}$"[draw=none],
- "${\varnothing}^{0}_{2.1.2}$"[draw=none]
+ a12/"${T}^{3}_{2}$" -- {
+ a121/"${T}^{4}_{2.1}$" -- {
+ a1211/"${a}^{0}_{2.1.1}$",
+ a1212/"${\varnothing}^{0}_{2.1.2}$"
}
}
}
};
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+ \node at (a11) {\xsp{2.5}\footnotesize{$\#0$}};
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+ \node at (a112) {\xsp{3.0}\footnotesize{$\#\infty$}};
+ \node at (a1121) {\xsp{3.5}\footnotesize{$\#\infty$}};
+ \node at (a12) {\xsp{2.5}\footnotesize{$\#1$}};
+ \node at (a121) {\xsp{3.0}\footnotesize{$\#1$}};
+ \node at (a1211) {\xsp{3.5}\footnotesize{$\#\infty$}};
+ \node at (a1212) {\xsp{3.5}\footnotesize{$\#\infty$}};
+
\node[yshift=-1.5in, draw=none]
{\small{${T}^{1}\big(
{T}^{2}(
\big)$}};
\end{scope}
-\begin{scope}[xshift=4.2in, yshift=-4in]
- \node[xshift=-0.3in, draw=none] {$u:$};
+\begin{scope}[xshift=4.1in, yshift=-3.3in, sibling distance=0.6in]
+ \node[xshift=-0.2in, draw=none] {$u:$};
\graph [tree layout, grow=down, fresh nodes] {
- "${T}^{1}_{\Lambda}$" -- {
- "${T}^{2}_{1}$" -- {
- "${\epsilon}^{0}_{1.1}$"[draw=none],
- "${\varnothing}^{0}_{1.2}$"[draw=none]
+ a1/"${T}^{1}_{\Lambda}$" -- {
+ a11/"${T}^{2}_{1}$" -- {
+ a111/"${\epsilon}^{0}_{1.1}$",
+ a112/"${\varnothing}^{0}_{1.2}$"
},
- "${T}^{3}_{2}$" -- {
- "${T}^{4}_{2.1}$" -- {
- "${a}^{0}_{2.1.1}$"[draw=none],
- "${\varnothing}^{0}_{2.1.2}$"[draw=none]
+ a12/"${T}^{3}_{2}$" -- {
+ a121/"${T}^{4}_{2.1}$" -- {
+ a1211/"${a}^{0}_{2.1.1}$",
+ a1212/"${\varnothing}^{0}_{2.1.2}$"
},
- "${T}^{4}_{2.2}$" -- {
- "${\varnothing}^{0}_{2.2.1}$"[draw=none],
- "${\epsilon}^{0}_{2.2.2}$"[draw=none]
+ a122/"${T}^{4}_{2.2}$" -- {
+ a1221/"${\varnothing}^{0}_{2.2.1}$",
+ a1222/"${\epsilon}^{0}_{2.2.2}$"
}
}
}
};
+ \node at (a1) {\xsp{2.5}\footnotesize{$\#1$}};
+ \node at (a11) {\xsp{2.5}\footnotesize{$\#0$}};
+ \node at (a111) {\xsp{3.0}\footnotesize{$\#\infty$}};
+ \node at (a112) {\xsp{3.0}\footnotesize{$\#\infty$}};
+ \node at (a12) {\xsp{2.5}\footnotesize{$\#1$}};
+ \node at (a121) {\xsp{3.0}\footnotesize{$\#1$}};
+ \node at (a1211) {\xsp{3.5}\footnotesize{$\#\infty$}};
+ \node at (a1212) {\xsp{3.5}\footnotesize{$\#\infty$}};
+ \node at (a122) {\xsp{3.0}\footnotesize{$\#0$}};
+ \node at (a1221) {\xsp{3.5}\footnotesize{$\#\infty$}};
+ \node at (a1222) {\xsp{3.5}\footnotesize{$\#\infty$}};
+
\node[xshift=0.2in, yshift=-1.5in, draw=none]
{\small{${T}^{1}\big(
{T}^{2}(
\begin{document}
-\begin{tikzpicture}[>=stealth, ->, auto, node distance=0.2in]
+\begin{tikzpicture}[>=stealth]
\tikzstyle{every node}=[draw=none, shape=rectangle]
% $(\epsilon|a^{0,\infty})(a|\epsilon)^{0,\infty}$
\begin{scope}[xshift=0in, yshift=0in]
+ \draw [draw=none] (-1.5in,0) rectangle (6.5in,0);
+\end{scope}
+
+\begin{scope}[xshift=3.7in, yshift=-0.4in]
\node (a) {{
$\begin{aligned}
&\alpha
= \Phi_0 (s)
- = \Phi_0 \big(
- {T}^{1} (
- {T}^{2} (
- {\varnothing}^{0},
- {T}^{0}({a}^{0})
- ), {T}^{3}(
- {\varnothing}^{4}
- )
- )\big)
+% = \Phi_0 \big(
+% {T}^{1} (
+% {T}^{2} (
+% {\varnothing}^{0},
+% {T}^{0}({a}^{0})
+% ), {T}^{3}(
+% {\varnothing}^{4}
+% )
+% )\big)
&&\!\!\!\!=\;
\overbracket {\Xl_1 \Xl_2 }%^{\alpha_0}
\;a\;
\\[-0.4em]
&\beta
= \Phi_0 (t)
- = \Phi_0 \big(
- {T}^{1} (
- {T}^{2}(
- {\varnothing}^{0},
- {T}^{0}({\varnothing}^{0})
- ),
- {T}^{3}\big(
- {T}^{4}({a}^{0},{\varnothing}^{0})
- )
- )\big)
+% = \Phi_0 \big(
+% {T}^{1} (
+% {T}^{2}(
+% {\varnothing}^{0},
+% {T}^{0}({\varnothing}^{0})
+% ),
+% {T}^{3}\big(
+% {T}^{4}({a}^{0},{\varnothing}^{0})
+% )
+% )\big)
&&\!\!\!\!=\;
\overbracket { \Xl_1 \Xl_2 \Xr_1 \Xl_2 \Xl_3 }%^{\beta_0}
\;a\;
\\[-0.4em]
&\gamma
= \Phi_0 (u)
- = \Phi_0 \big(
- {T}^{1} (
- {T}^{2}(
- {\epsilon}^{0},
- {\varnothing}^{0}
- ),
- {T}^{3} (
- {T}^{4}({a}^{0},{\varnothing}^{0}),
- {T}^{4}({\varnothing}^{0}, {\epsilon}^{0})
- )
- )\big)
+% = \Phi_0 \big(
+% {T}^{1} (
+% {T}^{2}(
+% {\epsilon}^{0},
+% {\varnothing}^{0}
+% ),
+% {T}^{3} (
+% {T}^{4}({a}^{0},{\varnothing}^{0}),
+% {T}^{4}({\varnothing}^{0}, {\epsilon}^{0})
+% )
+% )\big)
&&\!\!\!\!=\;
\overbracket { \Xl_1 \Xl_2 \Xr_1 \Xl_2 \Xl_3 }%^{\gamma_0}
\;a\;
\setlength\tabcolsep{3pt}
%\renewcommand{\arraystretch}{1.1}
-\begin{scope}[xshift=0in, yshift=-1.75in]
+\begin{scope}[xshift=3.7in, yshift=-2.3in]
\node (a) {
$\begin{aligned}
&\begin{tabular}{c|ll}
\end{tabular}
&&\quad
\left[\begin{aligned}
- \rho_0 &= min (lasth (\Xl_1 \Xl_2), minh (\epsilon)) = min (2, \infty) = 2 \\[-0.3em]
- \rho'_0 &= min (lasth (\Xl_1 \Xl_2), minh (\Xr_1 \Xl_2 \Xl_3)) = min (2, 1) = 1 \\[-0.3em]
- \rho_1 &= min (\rho_0, minh (\Xr_1 \Xl_2 \Xm_2 \Xr_1 \Xr_0)) = min (2,0) = 0 \\[-0.3em]
+ \rho_0 &= min (lasth (\Xl_1 \Xl_2), minh (\epsilon)) = min (2, \infty) = 2 \\[-0.2em]
+ \rho'_0 &= min (lasth (\Xl_1 \Xl_2), minh (\Xr_1 \Xl_2 \Xl_3)) = min (2, 1) = 1 \\[-0.2em]
+ \rho_1 &= min (\rho_0, minh (\Xr_1 \Xl_2 \Xm_2 \Xr_1 \Xr_0)) = min (2,0) = 0 \\[-0.2em]
\rho'_1 &= min (\rho'_0, minh (\Xr_2 \Xr_1 \Xr_0)) = min (1,0) = 0
\end{aligned}\right.
\\[0.7em]
\end{tabular}
&&\quad
\left[\begin{aligned}
- \rho_0 &= -1 \\[-0.3em]
- \rho'_0 &= -1 \\[-0.3em]
- \rho_1 &= min (lasth (\Xr_2), minh (\Xr_1 \Xr_0)) = min (2,0) = 0 \\[-0.3em]
+ \rho_0 &= -1 \\[-0.2em]
+ \rho'_0 &= -1 \\[-0.2em]
+ \rho_1 &= min (lasth (\Xr_2), minh (\Xr_1 \Xr_0)) = min (2,0) = 0 \\[-0.2em]
\rho'_1 &= min (lasth (\Xr_2), minh (\Xl_3 \Xr_2 \Xr_1 \Xr_0)) = min (2,0) = 0
\end{aligned}\right.
\\[0.7em]
\end{tabular}
&&\quad
\left[\begin{aligned}
- \rho_0 &= min (lasth (\Xl_1 \Xl_2), minh (\epsilon)) = min (2, \infty) = 2 \\[-0.3em]
- \rho'_0 &= min (lasth (\Xl_1 \Xl_2), minh (\Xr_1 \Xl_2 \Xl_3)) = min (2, 1) = 1 \\[-0.3em]
- \rho_1 &= min (\rho_0, minh (\Xr_1 \Xl_2 \Xm_2 \Xr_1 \Xr_0)) = min (2,0) = 0 \\[-0.3em]
+ \rho_0 &= min (lasth (\Xl_1 \Xl_2), minh (\epsilon)) = min (2, \infty) = 2 \\[-0.2em]
+ \rho'_0 &= min (lasth (\Xl_1 \Xl_2), minh (\Xr_1 \Xl_2 \Xl_3)) = min (2, 1) = 1 \\[-0.2em]
+ \rho_1 &= min (\rho_0, minh (\Xr_1 \Xl_2 \Xm_2 \Xr_1 \Xr_0)) = min (2,0) = 0 \\[-0.2em]
\rho'_1 &= min (\rho'_0, minh (\Xr_2 \Xl_3 \Xr_2 \Xr_1 \Xr_0)) = min (1,0) = 0
\end{aligned}\right.
\end{aligned}$
-\tikzstyle{every node}=[draw=none, shape=rectangle, sibling distance=0, level distance=0, outer sep = 0]
+\tikzstyle{styleA}=[draw=none
+ , shape=rectangle
+ , rounded corners=4
+ , level distance=0.35in
+ , sibling distance=0.45in
+ , minimum size = 0.2in
+ , inner sep = 0pt
+ , outer sep = 0pt
+ ]
+\tikzstyle{styleB}=[->
+ %, color = lightgray
+ , rounded corners=3.5
+ %, line width = 0
+ , dash pattern = on 1pt off 2.5pt
+ ]
+\newcommand\w{\hspace{2em}}
\small{
-\begin{scope}[xshift=-3.5in, yshift=0.3in]
- \node[xshift=-0.2in, draw=none] {$s:$};
+\begin{scope}[xshift=0in, yshift=0in]
+ \tikzstyle{every node}=[styleA]
+ %\tikzstyle{every edge}=[draw=none]
+ \node[xshift=-0.4in, draw=none] {$s:$};
\graph [tree layout, grow=down, fresh nodes] {
- "${T}^{1}$" -- {
- "${T}^{2}$" -- {
- "${\varnothing}^{0}$"[draw=none],
- "${T}^{0}$"[draw=none] -- {
- "${a}^{0}$"[draw=none]
+ s1/"${T}^{1}$" -- {
+ s11/"${T}^{2}$" -- {
+ s111/"${\varnothing}^{0}$",
+ s112/"${T}^{0}$" -- {
+ s1121/"${a}^{0}$"
}
},
- "${T}^{3}$" -- {
- "${\varnothing}^{4}$"
+ s12/"${T}^{3}$" -- {
+ s121/"${\varnothing}^{4}$"
}
}
};
+ \node at (s1) {$\Xl_1 \w \Xr_0$};
+ \node at (s11) {$\Xl_2 \w \Xr_1$};
+ \node at (s12) {$\Xl_2 \w \Xr_1$};
+ \node at (s121) {$\Xl_3 \w \Xr_2$};
+ \draw [->, styleB] ($(s1.west)$)
+ -- ($(s1.south west)$)
+ -- ($(s11.north west)$)
+ -- ($(s11.west)$)
+ -- ($(s11.south west)$)
+ -- ($(s111.north west)$)
+ -- ($(s111.west)$)
+ -- ($(s111.south west)$)
+ -- ($(s111.south)$)
+ -- ($(s111.south east)$)
+ -- ($(s111.east)$)
+ -- ($(s111.north east)$)
+ -- ($(s11.south)$)
+ -- ($(s112.north west)$)
+ -- ($(s112.west)$)
+ -- ($(s112.south west)$)
+ -- ($(s1121.north west)$)
+ -- ($(s1121.west)$);
+ \draw [->, styleB] ($(s1121.east)$)
+ -- ($(s1121.north east)$)
+ -- ($(s112.south east)$)
+ -- ($(s112.east)$)
+ -- ($(s112.north east)$)
+ -- ($(s11.south east)$)
+ -- ($(s11.east)$)
+ -- ($(s11.north east)$)
+ -- ($(s1.south)$)
+ -- ($(s12.north west)$)
+ -- ($(s12.west)$)
+ -- ($(s12.south west)$)
+ -- ($(s121.north west)$)
+ -- ($(s121.west)$)
+ -- ($(s121.south west)$)
+ -- ($(s121.south)$)
+ -- ($(s121.south east)$)
+ -- ($(s121.east)$)
+ -- ($(s121.north east)$)
+ -- ($(s12.south east)$)
+ -- ($(s12.east)$)
+ -- ($(s12.north east)$)
+ -- ($(s1.south east)$)
+ -- ($(s1.east)$);
\end{scope}
-\begin{scope}[xshift=-3.5in, yshift=-0.85in]
- \node[xshift=-0.2in, draw=none] {$t:$};
+\begin{scope}[xshift=0in, yshift=-1.3in]
+ \tikzstyle{every node}=[styleA]
+ \node[xshift=-0.4in, draw=none] {$t:$};
\graph [tree layout, grow=down, fresh nodes] {
- "${T}^{1}$" -- {
- "${T}^{2}$" -- {
- "${\varnothing}^{0}$"[draw=none],
- "${T}^{0}$"[draw=none] -- {
- "${\varnothing}^{0}$"[draw=none]
+ t1/"${T}^{1}$" -- {
+ t11/"${T}^{2}$" -- {
+ t111/"${\varnothing}^{0}$",
+ t112/"${T}^{0}$" -- {
+ t1121/"${\varnothing}^{0}$"
}
},
- "${T}^{3}$" -- {
- "${T}^{4}$" -- {
- "${a}^{0}$"[draw=none],
- "${\varnothing}^{0}$"[draw=none]
+ t12/"${T}^{3}$" -- {
+ t121/"${T}^{4}$" -- {
+ t1211/"${a}^{0}$",
+ t1212/"${\varnothing}^{0}$"
}
}
}
};
+ \node at (t1) {$\Xl_1 \w \Xr_0$};
+ \node at (t11) {$\Xl_2 \w \Xr_1$};
+ \node at (t12) {$\Xl_2 \w \Xr_1$};
+ \node at (t121) {$\Xl_3 \w \Xr_2$};
+ \draw [->, styleB] ($(t1.west)$)
+ -- ($(t1.south west)$)
+ -- ($(t11.north west)$)
+ -- ($(t11.west)$)
+ -- ($(t11.south west)$)
+ -- ($(t111.north west)$)
+ -- ($(t111.west)$)
+ -- ($(t111.south west)$)
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+ -- ($(t111.north east)$)
+ -- ($(t11.south)$)
+ -- ($(t112.north west)$)
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+ -- ($(t112.south west)$)
+ -- ($(t1121.north west)$)
+ -- ($(t1121.west)$)
+ -- ($(t1121.south west)$)
+ -- ($(t1121.south)$)
+ -- ($(t1121.south east)$)
+ -- ($(t1121.east)$)
+ -- ($(t1121.north east)$)
+ -- ($(t112.south east)$)
+ -- ($(t112.east)$)
+ -- ($(t112.north east)$)
+ -- ($(t11.south east)$)
+ -- ($(t11.east)$)
+ -- ($(t11.north east)$)
+ -- ($(t1.south)$)
+ -- ($(t12.north west)$)
+ -- ($(t12.west)$)
+ -- ($(t12.south west)$)
+ -- ($(t121.north west)$)
+ -- ($(t121.west)$)
+ -- ($(t121.south west)$)
+ -- ($(t1211.north west)$)
+ -- ($(t1211.west)$);
+ \draw [->, styleB]
+ ($(t1211.east)$)
+ -- ($(t121.south)$)
+ -- ($(t1212.north west)$)
+ -- ($(t1212.west)$)
+ -- ($(t1212.south west)$)
+ -- ($(t1212.south)$)
+ -- ($(t1212.south east)$)
+ -- ($(t1212.east)$)
+ -- ($(t1212.north east)$)
+ -- ($(t121.south east)$)
+ -- ($(t121.east)$)
+ -- ($(t121.north east)$)
+ -- ($(t12.south east)$)
+ -- ($(t12.east)$)
+ -- ($(t12.north east)$)
+ -- ($(t1.south east)$)
+ -- ($(t1.east)$);
\end{scope}
-\begin{scope}[xshift=-3.5in, yshift=-2in]
- \node[xshift=-0.2in, draw=none] {$u:$};
+\begin{scope}[xshift=0in, yshift=-2.6in]
+ \tikzstyle{every node}=[styleA]
+ \node[xshift=-0.4in, draw=none] {$u:$};
\graph [tree layout, grow=down, fresh nodes] {
- "${T}^{1}$" -- {
- "${T}^{2}$" -- {
- "${\epsilon}^{0}$"[draw=none],
- "${\varnothing}^{0}$"[draw=none]
+ t1/"${T}^{1}$" -- {
+ t11/"${T}^{2}$" -- {
+ t111/"${\epsilon}^{0}$",
+ t112/"${\varnothing}^{0}$"
},
- "${T}^{3}$" -- {
- "${T}^{4}$" -- {
- "${a}^{0}$"[draw=none],
- "${\varnothing}^{0}$"[draw=none]
+ t12/"${T}^{3}$" -- {
+ t121/"${T}^{4}$" -- {
+ t1211/"${a}^{0}$",
+ t1212/"${\varnothing}^{0}$"
},
- "${T}^{4}$" -- {
- "${\varnothing}^{0}$"[draw=none],
- "${\epsilon}^{0}$"[draw=none]
+ t122/"${T}^{4}$" -- {
+ t1221/"${\varnothing}^{0}$",
+ t1222/"${\epsilon}^{0}$"
}
}
}
};
+ \node at (t1) {$\Xl_1 \w \Xr_0$};
+ \node at (t11) {$\Xl_2 \w \Xr_1$};
+ \node at (t12) {$\Xl_2 \w \Xr_1$};
+ \node at (t121) {$\Xl_3 \w \Xr_2$};
+ \node at (t122) {$\Xl_3 \w \Xr_2$};
+ \draw [->, styleB]
+ ($(t1.west)$)
+ -- ($(t1.south west)$)
+ -- ($(t11.north west)$)
+ -- ($(t11.west)$)
+ -- ($(t11.south west)$)
+ -- ($(t111.north west)$)
+ -- ($(t111.west)$)
+ -- ($(t111.south west)$)
+ -- ($(t111.south)$)
+ -- ($(t111.south east)$)
+ -- ($(t111.east)$)
+ -- ($(t111.north east)$)
+ -- ($(t11.south)$)
+ -- ($(t112.north west)$)
+ -- ($(t112.west)$)
+ -- ($(t112.south west)$)
+ -- ($(t112.south)$)
+ -- ($(t112.south east)$)
+ -- ($(t112.east)$)
+ -- ($(t112.north east)$)
+ -- ($(t11.south east)$)
+ -- ($(t11.east)$)
+ -- ($(t11.north east)$)
+ -- ($(t1.south)$)
+ -- ($(t12.north west)$)
+ -- ($(t12.west)$)
+ -- ($(t12.south west)$)
+ -- ($(t121.north west)$)
+ -- ($(t121.west)$)
+ -- ($(t121.south west)$)
+ -- ($(t1211.north west)$)
+ -- ($(t1211.west)$);
+ \draw [->, styleB]
+ ($(t1211.east)$)
+ -- ($(t121.south)$)
+ -- ($(t1212.north west)$)
+ -- ($(t1212.west)$)
+ -- ($(t1212.south west)$)
+ -- ($(t1212.south)$)
+ -- ($(t1212.south east)$)
+ -- ($(t1212.east)$)
+ -- ($(t1212.north east)$)
+ -- ($(t121.south east)$)
+ -- ($(t121.east)$)
+ -- ($(t121.north east)$)
+ -- ($(t12.south)$)
+ -- ($(t122.north west)$)
+ -- ($(t122.west)$)
+ -- ($(t122.south west)$)
+ -- ($(t1221.north west)$)
+ -- ($(t1221.west)$)
+ -- ($(t1221.south west)$)
+ -- ($(t1221.south)$)
+ -- ($(t1221.south east)$)
+ -- ($(t1221.east)$)
+ -- ($(t1221.north east)$)
+ -- ($(t122.south)$)
+ -- ($(t1222.north west)$)
+ -- ($(t1222.west)$)
+ -- ($(t1222.south west)$)
+ -- ($(t1222.south)$)
+ -- ($(t1222.south east)$)
+ -- ($(t1222.east)$)
+ -- ($(t1222.north east)$)
+ -- ($(t122.south east)$)
+ -- ($(t122.east)$)
+ -- ($(t122.north east)$)
+ -- ($(t12.south east)$)
+ -- ($(t12.east)$)
+ -- ($(t12.north east)$)
+ -- ($(t1.south east)$)
+ -- ($(t1.east)$);
\end{scope}
}
\begin{document}
-\begin{tikzpicture}[>=stealth, auto, sibling distance = 0.3in, inner sep = 1.5pt]
+\begin{tikzpicture}[>=stealth, auto, sibling distance = 0.2in, inner sep = 1pt, outer sep = 0pt]
\tikzstyle{every node}=[draw, shape = circle]
-\begin{scope}[xshift=0in, yshift=0in]
- \graph [tree layout, grow=down, fresh nodes] {
- "$t_1$"[draw] -- {
- ""[draw] -- {
- ""[draw] -- { "$a$", "$a$", "$a$" }
+\small{
+\begin{scope}[xshift=0in, yshift=-0in]
+ \tikzstyle{every node}=[draw, shape = circle]
+ \graph [tree layout, grow=down, fresh nodes, level distance = 0.2in] {
+ "$t_1$" -- {
+ "" -- {
+ "" -- { "$a$", "$a$", "$a$" }
}
}
- , "$t_2$"[draw] -- {
- ""[draw] -- {
- ""[draw] -- { "$a$", "$a$" },
- ""[draw] -- { "$a$" }
+ , "$t_2$" -- {
+ "" -- {
+ "" -- { "$a$", "$a$" },
+ "" -- { "$a$" }
}
}
- , "$t_3$"[draw] -- {
- ""[draw] -- {
- ""[draw] -- { "$a$" },
- ""[draw] -- { "$a$", "$a$" }
+ , t31/"$t_3$" -- {
+ t311/"" -- {
+ t3111/"" -- { t31111/"$a$" },
+ t3112/"" -- { t31121/"$a$", t31122/"$a$" }
}
}
- , "$t_4$"[draw] -- {
- ""[draw] -- {
- ""[draw] -- { "$a$" },
- ""[draw] -- { "$a$" },
- ""[draw] -- { "$a$" }
+ , "$t_4$" -- {
+ "" -- {
+ "" -- { "$a$" },
+ "" -- { "$a$" },
+ "" -- { "$a$" }
}
}
- , "$t_5$"[draw] -- {
- ""[draw] -- {
- ""[draw] -- { "$a$", "$a$" }
+ , t51/"$t_5$" -- {
+ t511/"" -- {
+ t5111/"" -- { t51111/"$a$", t51112/"$a$" }
},
- ""[draw] -- {
- ""[draw] -- { "$a$" }
+ t512/"" -- {
+ t5121/"" -- { t51211/"$a$" }
}
}
- , "$t_6$"[draw] -- {
- ""[draw] -- {
- ""[draw] -- { "$a$" }
+ , "$t_6$" -- {
+ "" -- {
+ "" -- { "$a$" }
},
- ""[draw] -- {
- ""[draw] -- { "$a$", "$a$" }
+ "" -- {
+ "" -- { "$a$", "$a$" }
}
}
- , "$t_7$"[draw] -- {
- ""[draw] -- {
- ""[draw] -- { "$a$"},
- ""[draw] -- { "$a$"}
+ , "$t_7$" -- {
+ "" -- {
+ "" -- { "$a$"},
+ "" -- { "$a$"}
},
- ""[draw] -- {
- ""[draw] -- { "$a$" }
+ "" -- {
+ "" -- { "$a$" }
}
}
- , "$t_8$"[draw] -- {
- ""[draw] -- {
- ""[draw] -- { "$a$"}
+ , "$t_8$" -- {
+ "" -- {
+ "" -- { "$a$"}
},
- ""[draw] -- {
- ""[draw] -- { "$a$"},
- ""[draw] -- { "$a$" }
+ "" -- {
+ "" -- { "$a$"},
+ "" -- { "$a$" }
}
}
- , "$t_9$"[draw] -- {
- ""[draw] -- {
- ""[draw] -- { "$a$" }
+ , "$t_9$" -- {
+ "" -- {
+ "" -- { "$a$" }
},
- ""[draw] -- {
- ""[draw] -- { "$a$" }
+ "" -- {
+ "" -- { "$a$" }
},
- ""[draw] -- {
- ""[draw] -- { "$a$" }
+ "" -- {
+ "" -- { "$a$" }
}
}
};
\end{scope}
+}
-\tikzstyle{styleD}=[rounded corners, thick, dash pattern=on 1pt off 3pt]
-\tikzstyle{styleC}=[rounded corners, thick, dash pattern=on 3pt off 2pt]
-\tikzstyle{styleB}=[rounded corners, thick, dash pattern=on 5pt off 2pt]
-\tikzstyle{styleA}=[rounded corners, thick, dash pattern=on 8pt off 2pt]
-\begin{scope}[xshift=0in, yshift=-3.35in]
-% \tikzstyle{every node}=[draw, shape=circle]
- \tikzstyle{every node}=[draw=none, shape=rectangle, inner sep = 0, level distance=0.45in]
- \graph [tree layout, grow=down, fresh nodes, sibling distance=0.45in] {
- a1/""[label=above:$t_3$]{} -- {
- a11/"" -- {
- a111/"" -- { a1111/""[label=below:$a$] },
- a112/"" -- { a1121/""[label=below:$a$], a1122/""[label=below:$a$] }
+\tikzstyle{styleA}=[draw=none
+ , shape=circle
+ , minimum size = 0.2in
+ , inner sep = 0pt
+ , outer sep = 0pt
+ ]
+
+\tikzstyle{styleB}=[->
+ , rounded corners=3.5
+ %, color = lightgray
+ , dash pattern = on 1pt off 2.5pt
+ ]
+
+\newcommand\w{\hspace{2em}}
+
+\begin{scope}[xshift=0in, yshift=-2.5in]
+ \tikzstyle{every node}=[draw = none, shape = circle, inner sep = 0]
+ \node[xshift=-0.4in, draw=none] {$t_3:$};
+ \graph [tree layout, grow=down, fresh nodes, sibling distance = 0.45in, level distance = 0.35in] {
+ t31/"$T^1$" -- {
+ t311/"$T^2$" -- {
+ t3111/"$T^3$" -- { t31111/"$a^4$" },
+ t3112/"$T^5$" -- { t31121/"$a^6$", t31122/"$a^7$" }
}
}
};
- \tikzstyle{every node}=[draw=none, shape=rectangle]
- \newcommand\e{1.3em}
- \node (x1) at (a1) {$\Xl_1 \hspace{\e} \Xr_0$};
- \node (x11) at (a11) {$\Xl_2 \hspace{\e} \Xr_1$};
- \node (x111) at (a111) {$\Xl_3 \hspace{\e} \Xr_2$};
- \node (x112) at (a112) {$\Xl_3 \hspace{\e} \Xr_2$};
- \node (x1111) at (a1111) {$\Xl_4 \hspace{\e} \Xr_3$};
- \node (x1121) at (a1121) {$\Xl_4 \hspace{\e} \Xr_3$};
- \node (x1122) at (a1122) {$\Xl_4 \hspace{\e} \Xr_3$};
-
- \newcommand\xxx{
- \tikzstyle{every node}=[outer sep=0]
- \newcommand\w{0.12}
- \draw [->, styleA, lightgray, very thick] ($(a1.center)+(-\w,0)$) -- ($(a11.center)+(-\w,0)$) -- ($(a111.center)+(-\w,0)$) -- ($(a1111.center)+(-\w,0)$);
- \draw [ styleB, lightgray, very thick] ($(a1111.center)+(\w,0)$) -- ($(a111.center)+(\w,0)$);
- \draw [->, styleB] ($(a111.center)+(\w,0)$) -- ($(a11.center)+(0,-0.18)$) -- ($(a112.center)+(-\w,0)$) -- ($(a1121)+(-\w,0)$);
- \draw [->, styleC] ($(a1121.center)+(\w,0)$) -- ($(a112.center)+(0,-0.18)$) -- ($(a1122.center)+(-\w,0)$);
- \draw [->, styleD] ($(a1122.center)+(\w,0)$) -- ($(a112.center)+(\w,0)$) -- ($(a11.center)+(\w,0)$) -- ($(a1.center)+(\w,0)$);
- }
- \xxx
-
-% \node (f) [draw, shape=ellipse, fill] at ($(a111.center)+(\w,0)$) {};
+ \node at (t31) [styleA] {$\Xl_1 \w \Xr_0$};
+ \node at (t311) [styleA] {$\Xl_2 \w \Xr_1$};
+ \node at (t3111) [styleA] {$\Xl_3 \w \Xr_2$};
+ \node at (t3112) [styleA] {$\Xl_3 \w \Xr_2$};
+ \node at (t31111) [styleA] {$\Xl_4 \w \Xr_3$};
+ \node at (t31121) [styleA] {$\Xl_4 \w \Xr_3$};
+ \node at (t31122) [styleA] {$\Xl_4 \w \Xr_3$};
+ %
+ \node at (t31) [styleA] (tt31) {};
+ \node at (t311) [styleA] (tt311) {};
+ \node at (t3111) [styleA] (tt3111) {};
+ \node at (t3112) [styleA] (tt3112) {};
+ \node at (t31111) [styleA] (tt31111) {};
+ \node at (t31121) [styleA] (tt31121) {};
+ \node at (t31122) [styleA] (tt31122) {};
+ %
+ \draw [->, styleB] ($(tt31.west)$)
+ -- ($(tt311.west)$)
+ -- ($(tt3111.west)$)
+ -- ($(tt31111.west)$);
+ \draw [->, styleB] ($(tt31111.east)$)
+ -- ($(tt3111.east)$)
+ -- ($(tt311.south)$)
+ -- ($(tt3112.west)$)
+ -- ($(tt31121.west)$);
+ \draw [->, styleB] ($(tt31121.east)$)
+ -- ($(tt3112.south)$)
+ -- ($(tt31122.west)$);
+ \draw [->, styleB] ($(tt31122.east)$)
+ -- ($(tt3112.east)$)
+ -- ($(tt311.east)$)
+ -- ($(tt31.east)$);
\end{scope}
-\begin{scope}[xshift=1.65in, yshift=-3.35in]
-% \tikzstyle{every node}=[draw, shape=circle]
- \tikzstyle{every node}=[draw=none, shape=rectangle, inner sep = 0, level distance=0.45in]
- \graph [tree layout, grow=down, fresh nodes, sibling distance=0.45in] {
- b1/""[label=above:$t_5$]{} -- {
- b11/"" -- {
- b111/"" -- { b1111/""[label=below:$a$]{}, b1112/""[label=below:$a$] }
+\begin{scope}[xshift=1.6in, yshift=-2.5in]
+ \tikzstyle{every node}=[draw = none, shape = circle, inner sep = 0]
+ \node[xshift=-0.4in, draw=none] {$t_5:$};
+ \graph [tree layout, grow=down, fresh nodes, sibling distance = 0.45in, level distance = 0.35in] {
+ t51/"$T^1$" -- {
+ t511/"$T^2$" -- {
+ t5111/"$T^3$" -- { t51111/"$a^4$", t51112/"$a^5$" }
},
- b12/"" -- {
- b121/"" -- { b1211/""[label=below:$a$] }
+ t512/"$T^6$" -- {
+ t5121/"$T^7$" -- { t51211/"$a^8$" }
}
}
};
- \tikzstyle{every node}=[draw=none, shape=rectangle]
- \newcommand\e{1.3em}
- \node (y1) at (b1) {$\Xl_1 \hspace{\e} \Xr_0$};
- \node (y11) at (b11) {$\Xl_2 \hspace{\e} \Xr_1$};
- \node (y12) at (b12) {$\Xl_2 \hspace{\e} \Xr_1$};
- \node (y111) at (b111) {$\Xl_3 \hspace{\e} \Xr_2$};
- \node (y121) at (b121) {$\Xl_3 \hspace{\e} \Xr_2$};
- \node (y1111) at (b1111) {$\Xl_4 \hspace{\e} \Xr_3$};
- \node (y1112) at (b1112) {$\Xl_4 \hspace{\e} \Xr_3$};
- \node (y1211) at (b1211) {$\Xl_4 \hspace{\e} \Xr_3$};
-
- \newcommand\yyy{
- \tikzstyle{every node}=[outer sep=0]
- \newcommand\w{0.12}
- \draw [->, lightgray, very thick, styleA] ($(b1.center)+(-\w,0)$) -- ($(b11.center)+(-\w,0)$) -- ($(b111.center)+(-\w,0)$) -- ($(b1111.center)+(-\w,0)$);
- \draw [ lightgray, very thick, styleB] ($(b1111.center)+(\w,0)$) -- ($(b111.center)+(0,-0.18)$);
- \draw [->, styleB] ($(b111.center)+(0,-0.18)$) -- ($(b1112.center)+(-\w,0)$);
- \draw [->, styleC] ($(b1112.center)+(\w,0)$) -- ($(b111.center)+(\w,0)$) -- ($(b11.center)+(\w,0)$) -- ($(b1.center)+(0,-0.18)$)
- -- ($(b12.center)+(-\w,0)$) -- ($(b121.center)+(-\w,0)$) -- ($(b1211.center)+(-\w,0)$);
- \draw [->, styleD] ($(b1211.center)+(\w,0)$) -- ($(b121.center)+(\w,0)$) -- ($(b12.center)+(\w,0)$) -- ($(b1.center)+(\w,0)$);
- }
- \yyy
-
-% \node (f) [draw, shape=ellipse, fill] at ($(b111.center)+(0,-0.25)$) {};
-\end{scope}
-
-\begin{scope}[xshift=2.8in, yshift=-4.95in]
- \tikzstyle{every node}=[draw=none, shape=rectangle]
- \newcommand\z{0.3}
- \node (a1) at (0,0) {};
- \node at ($(a1)+(0,5*\z)$) [label=left:{{frame 0}}]{};
- \draw[->, styleA] ($(a1)+(0,5*\z)+(0,0)$) -- ($(a1)+(0,5*\z)+(1.2,0)$);
- \node at ($(a1)+(0,4*\z)$) [label=left:{{frame 1}}]{};
- \draw[->, styleB] ($(a1)+(0,4*\z)+(0,0)$) -- ($(a1)+(0,4*\z)+(1.2,0)$);
- \node at ($(a1)+(0,3*\z)$) [label=left:{{frame 2}}]{};
- \draw[->, styleC] ($(a1)+(0,3*\z)+(0,0)$) -- ($(a1)+(0,3*\z)+(1.2,0)$);
- \node at ($(a1)+(0,2*\z)$) [label=left:{{frame 3}}]{};
- \draw[->, styleD] ($(a1)+(0,2*\z)+(0,0)$) -- ($(a1)+(0,2*\z)+(1.2,0)$);
+ \node at (t51) [styleA] {$\Xl_1 \w \Xr_0$};
+ \node at (t511) [styleA] {$\Xl_2 \w \Xr_1$};
+ \node at (t5111) [styleA] {$\Xl_3 \w \Xr_2$};
+ \node at (t51111) [styleA] {$\Xl_4 \w \Xr_3$};
+ \node at (t51112) [styleA] {$\Xl_4 \w \Xr_3$};
+ \node at (t512) [styleA] {$\Xl_2 \w \Xr_1$};
+ \node at (t5121) [styleA] {$\Xl_3 \w \Xr_2$};
+ \node at (t51211) [styleA] {$\Xl_4 \w \Xr_3$};
+ %
+ \node at (t51) [styleA] (tt51) {};
+ \node at (t511) [styleA] (tt511) {};
+ \node at (t5111) [styleA] (tt5111) {};
+ \node at (t51111) [styleA] (tt51111) {};
+ \node at (t51112) [styleA] (tt51112) {};
+ \node at (t512) [styleA] (tt512) {};
+ \node at (t5121) [styleA] (tt5121) {};
+ \node at (t51211) [styleA] (tt51211) {};
+ %
+ \draw [->, styleB] ($(tt51.west)$)
+ -- ($(tt511.west)$)
+ -- ($(tt5111.west)$)
+ -- ($(tt51111.west)$);
+ \draw [->, styleB] ($(tt51111.east)$)
+ -- ($(tt5111.south)$)
+ -- ($(tt51112.west)$);
+ \draw [->, styleB] ($(tt51112.east)$)
+ -- ($(tt5111.east)$)
+ -- ($(tt511.east)$)
+ -- ($(tt51.south)$)
+ -- ($(tt512.west)$)
+ -- ($(tt5121.west)$)
+ -- ($(tt51211.west)$);
+ \draw [->, styleB] ($(tt51211.east)$)
+ -- ($(tt5121.east)$)
+ -- ($(tt512.east)$)
+ -- ($(tt51.east)$);
\end{scope}
-%\begin{scope}[xshift=0in, yshift=0.1in]
-% \node (a1) {1};
-% \node [right of = a1, xshift = 0.5in] (a2) {2};
-% \node [right of = a2, xshift = 0.35in] (a3) {3};
-% \node [right of = a3, xshift = 0.45in] (a4) {4};
-% \node [right of = a4, xshift = 0.45in] (a5) {5};
-%\end{scope}
-\begin{scope}[xshift=6.7in, yshift=-3.2in]
+\begin{scope}[xshift=5.7in, yshift=-2.3in]
\node [shape=rectangle, draw = none] (a) {
$\begin{aligned}
&\begin{aligned}
- &t_1 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
- &t_2 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
- &t_3 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
- &t_4 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
- &t_5 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
- &t_6 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
- &t_7 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
- &t_8 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
- &t_9 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0}
+ &\Phi_0(t_1) = \overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+ &\Phi_0(t_2) = \overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+ &\Phi_0(t_3) = \overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+ &\Phi_0(t_4) = \overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+ &\Phi_0(t_5) = \overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+ &\Phi_0(t_6) = \overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+ &\Phi_0(t_7) = \overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+ &\Phi_0(t_8) = \overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+ &\Phi_0(t_9) = \overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0}
\end{aligned}
\\[1em]
& \quad\quad t_1 < t_2 < t_3 < t_4 < t_5 < t_7 < t_6 < t_8 < t_9
};
\end{scope}
-\begin{scope}[xshift=2.4in, yshift=-3.1in]
+\begin{scope}[xshift=2.1in, yshift=-2.2in]
\node [shape=rectangle, draw = none] (a) {
- \setlength\tabcolsep{2pt}
+ \setlength\tabcolsep{1.5pt}
\renewcommand{\arraystretch}{1.1}
$\begin{aligned}
&\begin{tabular}{c ccccccccc}
All possible IPTs for RE $(((a)^{1,3})^{1,3})^{1,3}$ and string $aaa$, the corresponding PEs,\\
and the table of traces for each pair of PEs.
Table entry for row $t_i$ and column $t_j$ contains $traces(\Phi_0(t_i), \Phi_0(t_j))$.\\
-IPTs $t_3$ and $t_5$ are showed in more detail
-(dashed lines correspond to frames);
-traces for them are marked in bold.
+$t_3$ and $t_5$ are shown in more detail:
+dotted paths correspond to frames and the table entry is in bold.
}
\end{figure}
projects / re2c / commitdiff