be delivered. What I mean is that our algorithm can do it, and this is more general than Posix subexpressions.
Indeed, it can go from full-parsing to any user-defined submatch extraction.
+- Definition 17: F is used both to denote the set of final states and the function defined in Figure 2.
+ Perhaps it could be better to use two letters?
+
+- Figure 2,
+ - first graph: in it F(i,j,r) is defined for i != 0. However, an F with a first argument that is not zero is
+ never used. Perhaps there is a need to give some explanation
+ - graph for alternative: why the tags are defined only in the incoming arc of the second term, and the ougoing of the first?
+
+- in Figure 3:
+ - in match(), closure is called with a first argument that should
+be the set containing the initial
+ configuration, that in the call is a 4-tuple. However, closure
+expects configurations as 2-ples.
+ - in the first configuration there is a t_0 that is not defined
+ - reach() is called with three arguments, while in its definition
+it has two. I think that its signature
+ should be reach(X,Delta,alpha).
+ Configurations are 4-ples: (origin-state, target-state,
+input-symbol, tag), correct? The origin-state
+ is there for precedence(), and was the 'origin' in the pseudocode.
+
+- in Figure 4, closure_goldberg_radzik should be closure, and it
+should handle 4-ples configurations.
+Figure 4:
+
+ - relax. At the beginning all the values of result() are _|_, thus
+relax() should take care of it.
+ I suggest to replace the first two lines with:
+
+ if relax = _|_ or precedence(x,result(q),B,D then
+
+ - closure_goldberg_radzik, 2nd and 3rd lines: here result and status
+are initialized for all the states.
+ To prevent some reviewer to point out that "q" is not defined, I
+suggest to enclose the two
+ statements in a foreach q in Q
+ - same, line 14: here scan() is called, which in turn calls relax(),
+which accesses "status". Thus,
+ "status" should be passed as argument to both
+
+ - relax: its signature has B and D as last 5th and 6th arguments, but
+they are never passed when called.
+ They should be passed all along closure_goldberg_radzik and scan.
+
+ Comparing it with calc_rho_prec() in the pseudocode:
+ - the first two "if" statements can be merged
+ - the statement: h_1 = h_2 = height(...) can only be executed if k >
+1 (otherwise it accesses a_0 ...)
+ - the statement: "if a_k > b_k then l = -1" and the following, are
+different from the ones in the
+ pseudocode (if nonnegative (a[i]) return LT, etc.)
+ Comparing it with update_rho in the pseudocode:
+ - the pseudocode initializes h_1 and h_2 with the values read from
+B, while here it does so when
+ k > 1, which is never the case when q_1 != q_2
+
+
+- the statement: "if a_k > b_k then l = -1" and the following, are
+ different from the ones in the pseudocode (if nonnegative (a[i]) return LT, etc.)
+
\begin{scope}[xshift=0in, yshift=0in]
\node (a) {{
$\begin{aligned}
- \quad\quad
- & \Phi_0 \big(
+ &\alpha
+ = \Phi_0 (s)
+ = \Phi_0 \big(
{T}^{1} (
{T}^{2} (
{\varnothing}^{0},
), {T}^{3}(
{\varnothing}^{4}
)
- )\big) &&=
- \Xl_1
- \Xl_2
- a
- \Xr_1
- \Xl_2
- \Xm_2
- \Xr_1
- \Xr_0
- &&= \overbracket {\Xl_1 \Xl_2 }%^{\alpha_0}
- && a
- && \overbracket { \Xr_1 \Xl_2 \Xm_2 \Xr_1 \Xr_0 }%^{\alpha_1}
-% &&= \alpha_0 a \alpha_1
- &&= \alpha
+ )\big)
+ &&\!\!\!\!=\;
+ \overbracket {\Xl_1 \Xl_2 }%^{\alpha_0}
+ \;a\;
+ \overbracket { \Xr_1 \Xl_2 \Xm_2 \Xr_1 \Xr_0 }%^{\alpha_1}
\\[-0.4em]
- & \Phi_0 \big(
+ &\beta
+ = \Phi_0 (t)
+ = \Phi_0 \big(
{T}^{1} (
{T}^{2}(
{\varnothing}^{0},
{T}^{3}\big(
{T}^{4}({a}^{0},{\varnothing}^{0})
)
- )\big) &&=
- \Xl_1
- \Xl_2
- \Xr_1
- \Xl_2
- \Xl_3
- a
- \Xr_2
- \Xr_1
- \Xr_0
- &&= \overbracket { \Xl_1 \Xl_2 \Xr_1 \Xl_2 \Xl_3 }%^{\beta_0}
- && a
- && \overbracket { \Xr_2 \Xr_1 \Xr_0 }%^{\beta_1}
-% &&= \beta_0 a \beta_1
- &&= \beta
+ )\big)
+ &&\!\!\!\!=\;
+ \overbracket { \Xl_1 \Xl_2 \Xr_1 \Xl_2 \Xl_3 }%^{\beta_0}
+ \;a\;
+ \overbracket { \Xr_2 \Xr_1 \Xr_0 }%^{\beta_1}
\\[-0.4em]
- & \Phi_0 \big(
+ &\gamma
+ = \Phi_0 (u)
+ = \Phi_0 \big(
{T}^{1} (
{T}^{2}(
{\epsilon}^{0},
{T}^{4}({a}^{0},{\varnothing}^{0}),
{T}^{4}({\varnothing}^{0}, {\epsilon}^{0})
)
- )\big) &&=
- \Xl_1
- \Xl_2
- \Xr_1
- \Xl_2
- \Xl_3
- a
- \Xr_2
- \Xl_3
- \Xr_2
- \Xr_1
- \Xr_0
- &&= \overbracket { \Xl_1 \Xl_2 \Xr_1 \Xl_2 \Xl_3 }%^{\gamma_0}
- && a
- && \overbracket { \Xr_2 \Xl_3 \Xr_2 \Xr_1 \Xr_0 }%^{\gamma_1}
-% &&= \gamma_0 a \gamma_1
- &&= \gamma
- \quad\quad
+ )\big)
+ &&\!\!\!\!=\;
+ \overbracket { \Xl_1 \Xl_2 \Xr_1 \Xl_2 \Xl_3 }%^{\gamma_0}
+ \;a\;
+ \overbracket { \Xr_2 \Xl_3 \Xr_2 \Xr_1 \Xr_0 }%^{\gamma_1}
\end{aligned}$
}};
\end{scope}
-\begin{scope}[xshift=0in, yshift=-1.7in]
+\setlength\tabcolsep{3pt}
+%\renewcommand{\arraystretch}{1.1}
+
+\begin{scope}[xshift=0in, yshift=-1.75in]
\node (a) {
$\begin{aligned}
&\begin{tabular}{c|ll}
\rho_1 &= min (\rho_0, minh (\Xr_1 \Xl_2 \Xm_2 \Xr_1 \Xr_0)) = min (2,0) = 0 \\[-0.3em]
\rho'_1 &= min (\rho'_0, minh (\Xr_2 \Xr_1 \Xr_0)) = min (1,0) = 0
\end{aligned}\right.
- \\[0.5em]
+ \\[0.7em]
&\begin{tabular}{c|ll}
$traces (\beta, \gamma)$ & 0 & 1 \\
\hline \\[-1em]
\rho_1 &= min (lasth (\Xr_2), minh (\Xr_1 \Xr_0)) = min (2,0) = 0 \\[-0.3em]
\rho'_1 &= min (lasth (\Xr_2), minh (\Xl_3 \Xr_2 \Xr_1 \Xr_0)) = min (2,0) = 0
\end{aligned}\right.
- \\[0.5em]
+ \\[0.7em]
&\begin{tabular}{c|ll}
$traces (\alpha, \gamma)$ & 0 & 1 \\
\hline \\[-1em]
};
\end{scope}
+
+
+\tikzstyle{every node}=[draw=none, shape=rectangle, sibling distance=0, level distance=0, outer sep = 0]
+
+\small{
+\begin{scope}[xshift=-3.5in, yshift=0.3in]
+ \node[xshift=-0.2in, 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]
+ }
+ },
+ "${T}^{3}$" -- {
+ "${\varnothing}^{4}$"
+ }
+ }
+ };
+\end{scope}
+
+\begin{scope}[xshift=-3.5in, yshift=-0.85in]
+ \node[xshift=-0.2in, 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]
+ }
+ },
+ "${T}^{3}$" -- {
+ "${T}^{4}$" -- {
+ "${a}^{0}$"[draw=none],
+ "${\varnothing}^{0}$"[draw=none]
+ }
+ }
+ }
+ };
+\end{scope}
+
+\begin{scope}[xshift=-3.5in, yshift=-2in]
+ \node[xshift=-0.2in, draw=none] {$u:$};
+ \graph [tree layout, grow=down, fresh nodes] {
+ "${T}^{1}$" -- {
+ "${T}^{2}$" -- {
+ "${\epsilon}^{0}$"[draw=none],
+ "${\varnothing}^{0}$"[draw=none]
+ },
+ "${T}^{3}$" -- {
+ "${T}^{4}$" -- {
+ "${a}^{0}$"[draw=none],
+ "${\varnothing}^{0}$"[draw=none]
+ },
+ "${T}^{4}$" -- {
+ "${\varnothing}^{0}$"[draw=none],
+ "${\epsilon}^{0}$"[draw=none]
+ }
+ }
+ }
+ };
+\end{scope}
+}
+
+
\end{tikzpicture}
\end{document}
\begin{document}
-\begin{tikzpicture}[>=stealth, ->, auto, sibling distance = 0.3in, inner sep = 1.5pt]
+\begin{tikzpicture}[>=stealth, auto, sibling distance = 0.3in, inner sep = 1.5pt]
\tikzstyle{every node}=[draw, shape = circle]
\begin{scope}[xshift=0in, yshift=0in]
\graph [tree layout, grow=down, fresh nodes] {
- "$1$"[draw] -- {
+ "$t_1$"[draw] -- {
""[draw] -- {
""[draw] -- { "$a$", "$a$", "$a$" }
}
}
- , "$2$"[draw] -- {
+ , "$t_2$"[draw] -- {
""[draw] -- {
""[draw] -- { "$a$", "$a$" },
""[draw] -- { "$a$" }
}
}
- , "$3$"[draw] -- {
+ , "$t_3$"[draw] -- {
""[draw] -- {
""[draw] -- { "$a$" },
""[draw] -- { "$a$", "$a$" }
}
}
- , "$4$"[draw] -- {
+ , "$t_4$"[draw] -- {
""[draw] -- {
""[draw] -- { "$a$" },
""[draw] -- { "$a$" },
""[draw] -- { "$a$" }
}
}
- , "$5$"[draw] -- {
+ , "$t_5$"[draw] -- {
""[draw] -- {
""[draw] -- { "$a$", "$a$" }
},
""[draw] -- { "$a$" }
}
}
- , "$6$"[draw] -- {
+ , "$t_6$"[draw] -- {
""[draw] -- {
""[draw] -- { "$a$" }
},
""[draw] -- { "$a$", "$a$" }
}
}
- , "$7$"[draw] -- {
+ , "$t_7$"[draw] -- {
""[draw] -- {
""[draw] -- { "$a$"},
""[draw] -- { "$a$"}
""[draw] -- { "$a$" }
}
}
- , "$8$"[draw] -- {
+ , "$t_8$"[draw] -- {
""[draw] -- {
""[draw] -- { "$a$"}
},
""[draw] -- { "$a$" }
}
}
- , "$9$"[draw] -- {
+ , "$t_9$"[draw] -- {
""[draw] -- {
""[draw] -- { "$a$" }
},
};
\end{scope}
-\begin{scope}[xshift=1in, yshift=0in]
- \draw [dash pattern = on 2pt off 2pt, rounded corners] (2,-0.3) -- (2,-1) -- (1.45,-1.9) -- (1.45,-2.75);
- \draw [dash pattern = on 2pt off 2pt, rounded corners] (1.75,-2.75) -- (1.75,-2) -- (2.2,-1.3) -- (2.6,-2) -- (2.3,-2.75);
- \draw [dash pattern = on 2pt off 2pt, rounded corners] (2.55,-2.8) -- (2.75,-2.3) -- (2.9,-2.8);
- \draw [dash pattern = on 2pt off 2pt, rounded corners] (3.2,-2.75) -- (2.9,-1.9) -- (2.35,-1) -- (2.35,-0.3);
+\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{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 ($(a111.center)+(\w,0)$) {};
+\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:$a$] }
+ },
+ b12/"" -- {
+ b121/"" -- { b1211/""[label=below:$a$] }
+ }
+ }
+ };
+ \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] ($(a1)+(0,2*\z)+(0,0)$) -- ($(a1)+(0,2*\z)+(1.2,0)$);
\end{scope}
%\begin{scope}[xshift=0in, yshift=0.1in]
% \node [right of = a4, xshift = 0.45in] (a5) {5};
%\end{scope}
-\begin{scope}[xshift=6.5in, yshift=-3.1in]
+\begin{scope}[xshift=6.7in, yshift=-3.2in]
\node [shape=rectangle, draw = none] (a) {
$\begin{aligned}
- &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} \\
- &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} \\
- &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} \\
- &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} \\
- &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} \\
- &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} \\
- &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} \\
- &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} \\
- &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}
+ &\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}
+ \end{aligned}
+ \\[1em]
+ & \quad\quad t_1 < t_2 < t_3 < t_4 < t_5 < t_7 < t_6 < t_8 < t_9
\end{aligned}$
};
\end{scope}
-\begin{scope}[xshift=2.2in, yshift=-3.1in]
+\begin{scope}[xshift=2.4in, yshift=-3.1in]
\node [shape=rectangle, draw = none] (a) {
\setlength\tabcolsep{2pt}
\renewcommand{\arraystretch}{1.1}
$\begin{aligned}
&\begin{tabular}{c ccccccccc}
- 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
+ $t_2$ & $t_3$ & $t_4$ & $t_5$ & $t_6$ & $t_7$ & $t_8$ & $t_9$ \\
%
\begin{tabular}{|cccc|}
\hline
-1 & 1 & 1 & 0 \\
\hline
\end{tabular}
- & 1
+ & $t_1$
\\[1em]
%
&
-1 & 1 & 1 & 0 \\
\hline
\end{tabular}
- & 2
+ & $t_2$
\\[1em]
%
& &
\hline
\end{tabular}
&
+ \bf{
\begin{tabular}{|cccc|}
\hline
-1 & 2 & 2 & 0 \\[-3pt]
-1 & 3 & 1 & 0 \\
\hline
\end{tabular}
+ }
&
\begin{tabular}{|cccc|}
\hline
-1 & 1 & 1 & 0 \\
\hline
\end{tabular}
- & 3
+ & $t_3$
\\[1em]
%
& & &
-1 & 1 & 1 & 0 \\
\hline
\end{tabular}
- & 4
+ & $t_4$
\\[1em]
%
& & & &
-1 & 1 & 1 & 0 \\
\hline
\end{tabular}
- & 5
+ & $t_5$
\\[1em]
%
& & & & &
-1 & \!-1 & 1 & 0 \\
\hline
\end{tabular}
- & 6
+ & $t_6$
\\[1em]
%
& & & & & &
-1 & 1 & 1 & 0 \\
\hline
\end{tabular}
- & 7
+ & $t_7$
\\[1em]
%
& & & & & & &
-1 & \!-1 & 1 & 0 \\
\hline
\end{tabular}
- & 8
+ & $t_8$
\end{tabular}
\end{aligned}$
};
projects / re2c / commitdiff