From: Ulya Trofimovich <skvadrik@gmail.com>
Date: Wed, 17 Oct 2018 21:29:31 +0000 (+0100)
Subject: Paper: tweaks in picture layout.
X-Git-Tag: 1.2~321
X-Git-Url: https://granicus.if.org/sourcecode?a=commitdiff_plain;h=27aadc4075b97b8d26b9d2fd3ca655016762b8e8;p=re2c

Paper: tweaks in picture layout.
---

diff --git a/re2c/doc/tdfa_v2/img/pe.tex b/re2c/doc/tdfa_v2/img/pe.tex
index 218997bc..c721a10c 100644
--- a/re2c/doc/tdfa_v2/img/pe.tex
+++ b/re2c/doc/tdfa_v2/img/pe.tex
@@ -42,10 +42,10 @@
 
 \small{
 \begin{scope}[xshift=0in, yshift=0in]
-    \tikzstyle{every node}=[styleA, sibling distance = 0.4in]
+    \tikzstyle{every node}=[styleA, sibling distance = 0.5in]
 
-    \begin{scope}[xshift=0in, yshift=0in]
-    \node[xshift=0in, yshift=-1.25in, draw=none] {$s = T^1 (T^2 (\varnothing^0, T^0 (a^0, a^0)))$};
+    \begin{scope}[xshift=-0.5in, yshift=0in]
+    \node[xshift=0in, yshift=-1.2in, draw=none] {$s = T^1 (T^2 (\varnothing^0, T^0 (a^0, a^0)))$};
     \graph [tree layout, grow=down, fresh nodes] {
         s1/"${T}^{1}$" -- {
             s11/"${T}^{2}$" -- {
@@ -79,7 +79,7 @@
         -- ($(s1.east)$);
     \end{scope}
 
-    \begin{scope}[xshift=1.6in, yshift=0in]
+    \begin{scope}[xshift=1in, yshift=0in]
     \node[xshift=0in, yshift=-0.9in, draw=none] {$t = T^1 (T^2 (a^0, \varnothing^0), T^2 (a^0, \varnothing^0))$};
     \graph [tree layout, grow=down, fresh nodes] {
         s1/"${T}^{1}$" -- {
@@ -120,10 +120,9 @@
         -- ($(s1.east)$);
     \end{scope}
 
-    \begin{scope}[xshift=4.5in, yshift=-0.65in]
-        \node (a) {{
+    \begin{scope}[xshift=2.7in, yshift=-0.2in]
+        \node (a) {
         $\begin{aligned}
-        &\begin{aligned}
             \alpha = \Phi_0(s) &=
                 \overbracket {\Xl_1 \Xl_2 }
                 a
@@ -137,10 +136,15 @@
                 \overbracket { \Xr_1 \Xl_2 }
                 a
                 \overbracket { \Xr_1 \Xr_0 }
-        \end{aligned}
-        \\
-        &traces (\alpha, \beta) =
-        \left[\begin{aligned}
+        \end{aligned}$
+        };
+    \end{scope}
+
+    \begin{scope}[xshift=5in, yshift=-0.4in]
+        \node (a) {
+        $\begin{aligned}
+        tr&aces (\alpha, \beta) : \\[-0.4em]
+        &\left[\begin{aligned}
             \rho_0   &= \rho'_0 = -1 \\[-0.4em]
             \rho_1   &= min (lasth(\Xl_1 \Xl_2), minh (\epsilon))    = min (2, \infty) = 2 \\[-0.4em]
             \rho'_1  &= min (lasth(\Xl_1 \Xl_2), minh (\Xr_1 \Xl_2)) = min (2, 1)      = 1 \\[-0.4em]
@@ -148,35 +152,38 @@
             \rho'_2  &= min (\rho'_1, minh (\Xr_1 \Xr_0)) = min (1, 0) = 0
         \end{aligned}\right.
         \end{aligned}$
-        }};
+        };
+    \end{scope}
+
+    \begin{scope}[xshift=4in, yshift=-1.05in]
+        \node (a) {
+        $\begin{aligned}
+        &\rho_1 > \rho'_1 \;\wedge\; \rho_2 = \rho'_2
+            \;\Rightarrow\; \alpha \sqsubset \beta
+            \;\Rightarrow\; \alpha < \beta
+        \\[-0.3em]
+        \|s\|^{Sub}_1 = 2 &> 1 = \|t\|^{Sub}_1 \wedge \|s\|^{Sub}_p = \|t\|^{Sub}_p \;\forall p < 1
+            \;\Rightarrow\; s <_1 t
+        \end{aligned}$
+        };
     \end{scope}
 \end{scope}
 }
 \normalsize{
 \node (x1)
     [ xshift=2.7in
-    , yshift=-1.45in
+    , yshift=-1.4in
     , draw=none
     ] {(a) -- Rule 1: longest precedence, RE $(a|aa)^{0,\infty}$ and string $aa$.
-        Order on IPTs: $s <_1 t$ because $\|s\|^{Sub}_1 = 2 > 1 = \|t\|^{Sub}_1$ 
-    };
-\node (x2)
-    [ below of = x1
-    , yshift=0.225in
-    , draw=none
-    ] {
-    and $\|s\|^{Sub}_p = \|t\|^{Sub}_p \;\forall p < 1$.
-    Order on PEs: $\alpha < \beta$ because
-        $\rho_1 > \rho'_1 \;\wedge\; \rho_2 = \rho'_2 \;\Rightarrow\; \alpha \sqsubset \beta$.
     };
 }
 
 
 \small{
 \begin{scope}[xshift=0in, yshift=-1.9in]
-    \tikzstyle{every node}=[styleA]
+    \tikzstyle{every node}=[styleA, sibling distance = 0.5in]
 
-    \begin{scope}[xshift=0in, yshift=0in]
+    \begin{scope}[xshift=-0.5in, yshift=0in]
     \node[xshift=0in, yshift=-0.6in, draw=none] {$s = T^1 (a^2, \varnothing^3)$};
     \graph [tree layout, grow=down, fresh nodes] {
         r1/"${T}^{1}$" -- {
@@ -199,7 +206,7 @@
         -- ($(r1.east)$);
     \end{scope}
 
-    \begin{scope}[xshift=1.6in, yshift=0in]
+    \begin{scope}[xshift=1in, yshift=0in]
     \node[xshift=0in, yshift=-0.6in, draw=none] {$t = T^1 (\varnothing^2, a^3)$};
     \graph [tree layout, grow=down, fresh nodes] {
         t1/"${T}^{1}$" -- {
@@ -222,10 +229,9 @@
         -- ($(t1.east)$);
     \end{scope}
 
-    \begin{scope}[xshift=4.5in, yshift=-0.4in]
-        \node (a) {{
+    \begin{scope}[xshift=2.7in, yshift=-0.0in]
+        \node (a) {
         $\begin{aligned}
-        &\begin{aligned}
             \alpha = \Phi_0(s) &=
                 \overbracket {\Xl_1 \Xl_2 }
                 a
@@ -235,52 +241,55 @@
                 \overbracket {\Xl_1 \Xm_1 \Xl_2 }
                 a
                 \overbracket { \Xr_1 \Xr_0 }
-        \end{aligned}
-        \\
-        &traces (\alpha, \beta) =
-        \left[\begin{aligned}
+        \end{aligned}$
+        };
+    \end{scope}
+
+    \begin{scope}[xshift=5in, yshift=-0.1in]
+        \node (a) {
+        $\begin{aligned}
+        tr&aces (\alpha, \beta) : \\[-0.4em]
+        &\left[\begin{aligned}
             \rho_0   &= min (lasth (\Xl_1), minh (\Xl_2))       = min (1, 2) = 1 \\[-0.4em]
             \rho'_0  &= min (lasth (\Xl_1), minh (\Xm_1 \Xl_2)) = min (1, 1) = 1 \\[-0.4em]
             \rho_1   &= min (\rho_0,  minh (\Xr_1 \Xm_1 \Xr_0)) = min (1, 0) = 0 \\[-0.4em]
             \rho'_1  &= min (\rho'_0, minh (\Xr_1 \Xr_0))       = min (1, 0) = 0
         \end{aligned}\right.
         \end{aligned}$
-        }};
+        };
     \end{scope}
 
+    \begin{scope}[xshift=4in, yshift=-0.7in]
+        \node (a) {
+        $\begin{aligned}
+        \rho_i = \rho'_i &\;\forall i
+            \;\wedge\; first(\alpha \backslash \beta) = \Xl < \Xm = first(\beta \backslash \alpha)
+            \;\Rightarrow\; \alpha \sim \beta \;\wedge\; \alpha \subset \beta
+            \;\Rightarrow\; \alpha < \beta
+        \\[-0.3em]
+        &\|s\|^{Sub}_1 = 1 > -1 = \|t\|^{Sub}_1 \wedge \|s\|^{Sub}_p = \|t\|^{Sub}_p \;\forall p < 1
+            \;\Rightarrow\; s <_1 t
+        \end{aligned}$
+        };
+    \end{scope}
 \end{scope}
 }
 \normalsize{
 \node (y1)
     [ xshift=2.7in
-    , yshift=-3.0in
+    , yshift=-2.95in
     , draw=none
     ] {(b) -- Rule 2: leftmost precedence, RE $(a)|(a)$ and string $a$.
-    Order on IPTs: $s <_1 t$ because
-        $\|s\|^{Sub}_1 = 1 > -1 = \|t\|^{Sub}_1$
-    };
-\node (y2)
-    [ below of = y1
-    , yshift=0.225in
-    , draw=none
-    ] {
-    and $\|s\|^{Sub}_p = \|t\|^{Sub}_p \;\forall p < 1$.
-    Order on PEs: $\alpha < \beta$ because
-        $\rho_i = \rho'_i \;\forall i \;\Rightarrow\; \alpha \sim \beta$
-        and
-        $first(\alpha \backslash \beta) = \Xl < \Xm = first(\beta \backslash \alpha)
-        \;\Rightarrow\;
-        \alpha \subset \beta$.
     };
 }
 
 
 \small{
-\begin{scope}[xshift=0in, yshift=-3.4in]
-    \tikzstyle{every node}=[styleA, sibling distance = 0.4in]
+\begin{scope}[xshift=0in, yshift=-3.3in]
+    \tikzstyle{every node}=[styleA, sibling distance = 0.5in]
 
+    \begin{scope}[xshift=-0.5in, yshift=0in]
     \node[yshift=-0.9in, draw=none] {$s = T^1(T^2(a^0, \varnothing^0))$};
-    \begin{scope}[xshift=0in, yshift=0in]
     \graph [tree layout, grow=down, fresh nodes] {
         s1/"${T}^{1}$" -- {
             s11/"${T}^{2}$" -- {
@@ -306,7 +315,7 @@
         -- ($(s1.east)$);
     \end{scope}
 
-    \begin{scope}[xshift=1.6in, yshift=0in]
+    \begin{scope}[xshift=1in, yshift=0in]
     \node[xshift=0in, yshift=-0.9in, draw=none] {$t = T^1 (T^2 (a^0, \varnothing^0), T^2(\varnothing^0, \epsilon^0))$};
     \graph [tree layout, grow=down, fresh nodes] {
         s1/"${T}^{1}$" -- {
@@ -347,10 +356,9 @@
         -- ($(s1.east)$);
     \end{scope}
 
-    \begin{scope}[xshift=4.5in, yshift=-0.45in]
-        \node (a) {{
+    \begin{scope}[xshift=2.7in, yshift=-0.2in]
+        \node (a) {
         $\begin{aligned}
-        &\begin{aligned}
             \alpha = \Phi_0(s) &=
                 \overbracket {\Xl_1 \Xl_2 }
                 a
@@ -360,52 +368,56 @@
                 \overbracket { \Xl_1 \Xl_2 }
                 a
                 \overbracket { \Xr_1 \Xl_2 \Xr_1 \Xr_0 }
-        \end{aligned}
-        \\
-        &traces (\alpha, \beta) =
-        \left[\begin{aligned}
+        \end{aligned}$
+        };
+    \end{scope}
+
+    \begin{scope}[xshift=5in, yshift=-0.2in]
+        \node (a) {
+        $\begin{aligned}
+        tr&aces (\alpha, \beta) :
+        \\[-0.4em]
+        &\left[\begin{aligned}
             \rho_0   &= \rho'_0 = -1 \\[-0.4em]
             \rho_1   &= min (lasth (\Xr_1), minh (\Xr_0))             = min (1, 0) = 0 \\[-0.4em]
             \rho'_1  &= min (lasth (\Xr_1), minh (\Xl_2 \Xr_1 \Xr_0)) = min (1, 0) = 0
         \end{aligned}\right.
         \end{aligned}$
-        }};
+        };
     \end{scope}
 
+    \begin{scope}[xshift=4in, yshift=-0.75in]
+        \node (a) {
+        $\begin{aligned}
+        \rho_i = \rho'_i \;\forall i
+            &\;\wedge\; first(\alpha \backslash \beta) = \Xr < \Xl = first(\beta \backslash \alpha)
+            \;\Rightarrow\; \alpha \sim \beta \;\wedge\; \alpha \subset \beta
+            \;\Rightarrow\; \alpha < \beta
+        \\[-0.3em]
+        &\|s\|^{Sub}_2 = \infty > 0 = \|t\|^{Sub}_2 \wedge \|s\|^{Sub}_p = \|t\|^{Sub}_p \;\forall p < 2
+            \;\Rightarrow\; s <_2 t
+        \end{aligned}$
+        };
+    \end{scope}
 \end{scope}
 }
 \normalsize{
 \node (z1)
     [ xshift=2.7in
-    , yshift=-4.5in
+    , yshift=-4.45in
     , draw=none
     ] {(c) -- Rule 3: no optional empty repetitions,
         RE $(a|\epsilon)^{0,\infty}$ and string $a$.
-        Order on IPTs: $s <_2 t$ because
-        $\|s\|^{Sub}_2 = \infty > 0 = \|t\|^{Sub}_2$
         };
-\node (z2)
-    [ below of = z1
-    , yshift=0.225in
-    , draw=none
-    ] {
-    and $\|s\|^{Sub}_p = \|t\|^{Sub}_p \;\forall p < 2$.
-    Order on PEs: $\alpha < \beta$ because
-        $\rho_i = \rho'_i \;\forall i \;\Rightarrow\; \alpha \sim \beta$
-        and
-        $first(\alpha \backslash \beta) = \Xr < \Xl = first(\beta \backslash \alpha)
-        \;\Rightarrow\;
-        \alpha \subset \beta$.
-    };
 }
 
 
 \small{
-\begin{scope}[xshift=0in, yshift=-4.9in]
-    \tikzstyle{every node}=[styleA, sibling distance = 0.4in]
+\begin{scope}[xshift=0in, yshift=-4.85in]
+    \tikzstyle{every node}=[styleA, sibling distance = 0.5in]
 
+    \begin{scope}[xshift=-0.5in, yshift=0in]
     \node[yshift=-0.6in, draw=none] {$s = T^1(\varnothing^2)$};
-    \begin{scope}[xshift=0in, yshift=0in]
     \graph [tree layout, grow=down, fresh nodes] {
         s1/"${T}^{1}$" -- {
             s11/"${\varnothing}^{2}$"
@@ -421,7 +433,7 @@
         -- ($(s1.east)$);
     \end{scope}
 
-    \begin{scope}[xshift=1.6in, yshift=0in]
+    \begin{scope}[xshift=1in, yshift=0in]
     \node[xshift=0in, yshift=-0.9in, draw=none] {$t = T^1(T^2(\epsilon^0))$};
     \graph [tree layout, grow=down, fresh nodes] {
         s1/"${T}^{1}$" -- {
@@ -447,51 +459,54 @@
         -- ($(s1.east)$);
     \end{scope}
 
-    \begin{scope}[xshift=4.5in, yshift=-0.45in]
-        \node (a) {{
+    \begin{scope}[xshift=2.7in, yshift=-0.2in]
+        \node (a) {
         $\begin{aligned}
-        &\begin{aligned}
             \alpha = \Phi_0(s) &=
                 \overbracket {\Xl_1 \Xm_1 \Xr_0 }
                 \\[-0.4em]
             \beta = \Phi_0(t) &=
                 \overbracket {\Xl_1 \Xl_2 \Xr_1 \Xr_0 }
-        \end{aligned}
-        \\
-        &traces (\alpha, \beta) =
-        \left[\begin{aligned}
+        \end{aligned}$
+        };
+    \end{scope}
+
+    \begin{scope}[xshift=5in, yshift=-0.2in]
+        \node (a) {
+        $\begin{aligned}
+        tr&aces (\alpha, \beta) :
+        \\[-0.4em]
+        &\left[\begin{aligned}
             \rho_0   &= min (lasth (\Xl_1), minh (\Xm_1 \Xr_0))       = min (1, 0) = 0 \\[-0.4em]
             \rho'_0  &= min (lasth (\Xl_1), minh (\Xl_2 \Xr_1 \Xr_0)) = min (1, 0) = 0
         \end{aligned}\right.
         \end{aligned}$
-        }};
+        };
     \end{scope}
 
+    \begin{scope}[xshift=4in, yshift=-0.7in]
+        \node (a) {
+        $\begin{aligned}
+        \rho_i = \rho'_i \;\forall i
+            &\;\wedge\; first(\alpha \backslash \beta) = \Xm > \Xl = first(\beta \backslash \alpha)
+            \;\Rightarrow\; \alpha \sim \beta \;\wedge\; \beta \subset \alpha
+            \;\Rightarrow\; \beta < \alpha
+        \\[-0.3em]
+        &\|s\|^{Sub}_2 = 0 > -1 = \|s\|^{Sub}_2 \wedge \|s\|^{Sub}_p = \|t\|^{Sub}_p \;\forall p < 2
+            \;\Rightarrow\; t <_2 s
+        \end{aligned}$
+        };
+    \end{scope}
 \end{scope}
 }
 \normalsize{
 \node (z1)
     [ xshift=2.7in
-    , yshift=-6.0in
+    , yshift=-6in
     , draw=none
     ] {(d) -- Rule 4: empty match is better than no match,
         RE $(a|\epsilon)^{0,\infty}$ and string $\epsilon$.
-        Order on IPTs: $t <_2 s$ because
-        $\|s\|^{Sub}_2 = 0 > -1 = \|s\|^{Sub}_2$
         };
-\node (z2)
-    [ below of = z1
-    , yshift=0.225in
-    , draw=none
-    ] {
-    and $\|s\|^{Sub}_p = \|t\|^{Sub}_p \;\forall p < 2$.
-    Order on PEs: $\beta < \alpha$ because
-        $\rho_i = \rho'_i \;\forall i \;\Rightarrow\; \alpha \sim \beta$
-        and
-        $first(\alpha \backslash \beta) = \Xm > \Xl = first(\beta \backslash \alpha)
-        \;\Rightarrow\;
-        \beta \subset \alpha$.
-    };
 }
 
 
@@ -590,7 +605,7 @@
     ]
 
 
-\begin{scope}[xshift=0in, yshift=-2.0in]
+\begin{scope}[xshift=0in, yshift=-2.2in]
     \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 = 0.3in] {
@@ -636,7 +651,7 @@
 \end{scope}
 
 
-\begin{scope}[xshift=1.6in, yshift=-2in]
+\begin{scope}[xshift=1.6in, yshift=-2.2in]
     \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 = 0.3in] {
@@ -688,7 +703,7 @@
 \end{scope}
 
 
-\begin{scope}[xshift=5.6in, yshift=-1.85in]
+\begin{scope}[xshift=5.6in, yshift=-2in]
     \node [shape=rectangle, draw = none] (a) {
     $\begin{aligned}
         &\begin{aligned}
@@ -709,13 +724,14 @@
 \end{scope}
 
 
-\begin{scope}[xshift=2.0in, yshift=-1.8in]
+\begin{scope}[xshift=2.0in, yshift=-1.9in]
     \node [shape=rectangle, draw = none] (a) {
     \setlength\tabcolsep{1.5pt}
     \renewcommand{\arraystretch}{0.5}
     $\begin{aligned}
         &\begin{tabular}{cccccccc|c}
               $t_2$ & $t_3$ & $t_4$ & $t_5$ & $t_6$ & $t_7$ & $t_8$ & $t_9$ \\
+              &&&&&&& \\[-0.4em]
               \hline
               &&&&&&& \\[-0.2em]
             %
@@ -930,12 +946,12 @@
 \normalsize{
 \node (w1)
     [ xshift=3.3in
-    , yshift=-3.2in
+    , yshift=-3.4in
     , draw=none
     , shape=rectangle
     ] {(e) --
-        All possible IPTs for RE $(((a)^{1,3})^{1,3})^{1,3}$ and string $aaa$, the corresponding PEs,
-        and the table of $traces(\Phi_0(t_i), \Phi_0(t_j))$
+        Pairwise comparison of all PEs for RE $(((a)^{1,3})^{1,3})^{1,3}$ and string $aaa$.
+        The table contains $traces(\Phi_0(t_i), \Phi_0(t_j))$
     };
 \node (w2)
     [ below of = w1
@@ -943,8 +959,8 @@
     , draw=none
     , shape=rectangle
     ] {
-        for each pair of PEs at row $t_i$, column $t_j$.
-        IPTs $t_3$ and $t_5$ are shown in more detail (their table entry is in bold).
+        for PEs at row $t_i$, column $t_j$.
+        IPTs $t_3$ and $t_5$ are shown in more detail (table entry in bold).
     };
 }