Paper: another example of traces computation.

diff --git a/re2c/doc/tdfa_v2/img/Makefile b/re2c/doc/tdfa_v2/img/Makefile
index 120d8c27db865cdda18537e7156649080d5dc85c..0656219e4497302b619addcc1b4054798d4f2338 100644 (file)
--- a/re2c/doc/tdfa_v2/img/Makefile
+++ b/re2c/doc/tdfa_v2/img/Makefile
@@ -1,7 +1,7 @@
 %.pdf : %.tex
        lualatex -shell-escape $< </dev/null > $<.build_log
 
-all : mark_enum.pdf pe.pdf trees.pdf tnfa.pdf gor1.pdf
+all : mark_enum.pdf pe.pdf pe2.pdf trees.pdf tnfa.pdf gor1.pdf
 
 clean:
        rm *.log *.build_log *.aux *.pdf *.pag

diff --git a/re2c/doc/tdfa_v2/img/pe.tex b/re2c/doc/tdfa_v2/img/pe.tex
index e4b69712a825517c7858cc29603c6185b24bde88..8980859bc3524381deb835909ed1aa81156f187d 100644 (file)
--- a/re2c/doc/tdfa_v2/img/pe.tex
+++ b/re2c/doc/tdfa_v2/img/pe.tex
@@ -23,14 +23,14 @@
 
 \begin{tikzpicture}[>=stealth, ->, auto, node distance=0.2in]
 
-\tikzstyle{every node}=[draw=none]
+\tikzstyle{every node}=[draw=none, shape=rectangle]
 
 % $(\epsilon|a^{0,\infty})(a|\epsilon)^{0,\infty}$
 
 \begin{scope}[xshift=0in, yshift=0in]
     \node (a) {{
     $\begin{aligned}
-        \quad
+        \quad\quad
         & \Phi_0 \big(
             {T}^{1} (
                 {T}^{2} (
@@ -53,7 +53,7 @@
             && \overbracket { \Xr_1 \Xl_2 \Xm_2 \Xr_1 \Xr_0 }%^{\alpha_1}
 %            &&= \alpha_0 a \alpha_1 
             &&= \alpha
-        \\[-0.3em]
+        \\[-0.4em]
         & \Phi_0 \big(
             {T}^{1} (
                 {T}^{2}(
@@ -78,7 +78,7 @@
             && \overbracket { \Xr_2 \Xr_1 \Xr_0 }%^{\beta_1}
 %            &&= \beta_0 a \beta_1
             &&= \beta
-        \\[-0.3em]
+        \\[-0.4em]
         & \Phi_0 \big(
             {T}^{1} (
                 {T}^{2}(
@@ -106,54 +106,54 @@
             && \overbracket { \Xr_2 \Xl_3 \Xr_2 \Xr_1 \Xr_0 }%^{\gamma_1}
 %            &&= \gamma_0 a \gamma_1
             &&= \gamma
-        \quad
+        \quad\quad
     \end{aligned}$
     }};
 \end{scope}
 
-\begin{scope}[xshift=0in, yshift=-2.1in]
+\begin{scope}[xshift=0in, yshift=-1.7in]
     \node (a) {
     $\begin{aligned}
         &\begin{tabular}{c|ll}
             $traces (\alpha, \beta)$ & 0 & 1 \\
-            \hline \\[-0.5em]
-            $\rho^{\alpha/\beta}$ & 2 & 0 \\
-            $\rho^{\beta/\alpha}$ & 1 & 0 \\
+            \hline \\[-1em]
+            $\rho$ & 2 & 0 \\
+            $\rho'$ & 1 & 0 \\
         \end{tabular}
         &&\quad
         \left[\begin{aligned}
-            \rho^{\alpha/\beta}_0  &= min (lasth (\Xl_1 \Xl_2), minh (\epsilon))          = min (2, \infty) = 2 \\[-0.3em]
-            \rho^{\beta/\alpha}_0  &= min (lasth (\Xl_1 \Xl_2), minh (\Xr_1 \Xl_2 \Xl_3)) = min (2, 1)      = 1 \\[-0.3em]
-            \rho^{\alpha/\beta}_1  &= min (\rho^{\alpha/\beta}_0, minh (\Xr_1 \Xl_2 \Xm_2 \Xr_1 \Xr_0)) = min (2,0) = 0 \\[-0.3em]
-            \rho^{\beta/\alpha}_1  &= min (\rho^{\beta/\alpha}_0, minh (\Xr_2 \Xr_1 \Xr_0))             = min (1,0) = 0
+            \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'_1  &= min (\rho'_0, minh (\Xr_2 \Xr_1 \Xr_0))             = min (1,0) = 0
         \end{aligned}\right.
-        \\[1em]
+        \\[0.5em]
         &\begin{tabular}{c|ll}
             $traces (\beta, \gamma)$ & 0 & 1 \\
-            \hline \\[-0.5em]
-            $\rho^{\beta/\gamma}$ & -1 & 0 \\
-            $\rho^{\gamma/\beta}$ & -1 & 0 \\
+            \hline \\[-1em]
+            $\rho$ & \!-1 & 0 \\
+            $\rho'$ & \!-1 & 0 \\
         \end{tabular}
         &&\quad
         \left[\begin{aligned}
-            \rho^{\beta/\gamma}_0  &= -1 \\[-0.3em]
-            \rho^{\gamma/\beta}_0  &= -1 \\[-0.3em]
-            \rho^{\beta/\gamma}_1  &= min (lasth (\Xr_2), minh (\Xr_1 \Xr_0))             = min (2,0) = 0 \\[-0.3em]
-            \rho^{\gamma/\beta}_1  &= min (lasth (\Xr_2), minh (\Xl_3 \Xr_2 \Xr_1 \Xr_0)) = min (2,0) = 0
+            \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'_1  &= min (lasth (\Xr_2), minh (\Xl_3 \Xr_2 \Xr_1 \Xr_0)) = min (2,0) = 0
         \end{aligned}\right.
-        \\[1em]
+        \\[0.5em]
         &\begin{tabular}{c|ll}
             $traces (\alpha, \gamma)$ & 0 & 1 \\
-            \hline \\[-0.5em]
-            $\rho^{\alpha/\gamma}$ & 2 & 0 \\
-            $\rho^{\gamma/\alpha}$ & 1 & 0 \\
+            \hline \\[-1em]
+            $\rho$ & 2 & 0 \\
+            $\rho'$ & 1 & 0 \\
         \end{tabular}
         &&\quad
         \left[\begin{aligned}
-            \rho^{\alpha/\gamma}_0  &= min (lasth (\Xl_1 \Xl_2), minh (\epsilon))          = min (2, \infty) = 2 \\[-0.3em]
-            \rho^{\gamma/\alpha}_0  &= min (lasth (\Xl_1 \Xl_2), minh (\Xr_1 \Xl_2 \Xl_3)) = min (2, 1)      = 1 \\[-0.3em]
-            \rho^{\alpha/\gamma}_1  &= min (\rho^{\alpha/\gamma}_0, minh (\Xr_1 \Xl_2 \Xm_2 \Xr_1 \Xr_0)) = min (2,0) = 0 \\[-0.3em]
-            \rho^{\gamma/\alpha}_1  &= min (\rho^{\gamma/\alpha}_0, minh (\Xr_2 \Xl_3 \Xr_2 \Xr_1 \Xr_0)) = min (1,0) = 0
+            \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'_1  &= min (\rho'_0, minh (\Xr_2 \Xl_3 \Xr_2 \Xr_1 \Xr_0)) = min (1,0) = 0
         \end{aligned}\right.
     \end{aligned}$
     };

diff --git a/re2c/doc/tdfa_v2/img/pe2.tex b/re2c/doc/tdfa_v2/img/pe2.tex
new file mode 100644 (file)
index 0000000..9be68fc
--- /dev/null
+++ b/re2c/doc/tdfa_v2/img/pe2.tex
@@ -0,0 +1,422 @@
+
+\documentclass[tikz,border=10pt]{standalone}
+
+
+\RequirePackage{luatex85}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath, amssymb, amsfonts, accents}
+\usetikzlibrary{graphdrawing, graphs, arrows, shapes, automata, calc}
+\usegdlibrary{trees, layered}
+\usepackage{stix}
+
+
+%\newcommand{\Xund}{\rule{.4em}{.4pt}}
+%\newcommand{\IRE}{I\!RE}
+
+\newcommand{\Xund}{\rule{.4em}{.4pt}}
+\newcommand{\Xl}{\langle}
+\newcommand{\Xr}{\rangle}
+\newcommand{\Xm}{\langle\!\rangle}
+
+
+\begin{document}
+
+\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] -- {
+            ""[draw] -- {
+                ""[draw] -- { "$a$", "$a$", "$a$" }
+            }
+        }
+        , "$2$"[draw] -- {
+            ""[draw] -- {
+                ""[draw] -- { "$a$", "$a$" },
+                ""[draw] -- { "$a$" }
+            }
+        }
+        , "$3$"[draw] -- {
+            ""[draw] -- {
+                ""[draw] -- { "$a$" },
+                ""[draw] -- { "$a$", "$a$" }
+            }
+        }
+        , "$4$"[draw] -- {
+            ""[draw] -- {
+                ""[draw] -- { "$a$" },
+                ""[draw] -- { "$a$" },
+                ""[draw] -- { "$a$" }
+            }
+        }
+        , "$5$"[draw] -- {
+            ""[draw] -- {
+                ""[draw] -- { "$a$", "$a$" }
+            },
+            ""[draw] -- {
+                ""[draw] -- { "$a$" }
+            }
+        }
+        , "$6$"[draw] -- {
+            ""[draw] -- {
+                ""[draw] -- { "$a$" }
+            },
+            ""[draw] -- {
+                ""[draw] -- { "$a$", "$a$" }
+            }
+        }
+        , "$7$"[draw] -- {
+            ""[draw] -- {
+                ""[draw] -- { "$a$"},
+                ""[draw] -- { "$a$"}
+            },
+            ""[draw] -- {
+                ""[draw] -- { "$a$" }
+            }
+        }
+        , "$8$"[draw] -- {
+            ""[draw] -- {
+                ""[draw] -- { "$a$"}
+            },
+            ""[draw] -- {
+                ""[draw] -- { "$a$"},
+                ""[draw] -- { "$a$" }
+            }
+        }
+        , "$9$"[draw] -- {
+            ""[draw] -- {
+                ""[draw] -- { "$a$" }
+            },
+            ""[draw] -- {
+                ""[draw] -- { "$a$" }
+            },
+            ""[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);
+\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=6.5in, yshift=-3.1in]
+    \node [shape=rectangle, draw = none] (a) {
+    $\begin{aligned}
+        &1 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+        &2 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+        &3 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+        &4 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+        &5 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+        &6 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+        &7 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+        &8 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0} \\
+        &9 &&\overbracket {\Xl_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xl_2 \Xl_3 \Xl_4} a \overbracket {\Xr_3 \Xr_2 \Xr_1 \Xr_0}
+    \end{aligned}$
+    };
+\end{scope}
+
+\begin{scope}[xshift=2.2in, 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 \\
+            %
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & \!-1 & 3 & 0 \\[-3pt]
+                -1 & \!-1 & 2 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 3 & 0 \\[-3pt]
+                -1 & 2 & 2 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 3 & 0 \\[-3pt]
+                -1 & 2 & 2 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & \!-1 & 3 & 0 \\[-3pt]
+                -1 & \!-1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 3 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 3 & 0 \\[-3pt]
+                -1 & 2 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 3 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 3 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            & 1
+            \\[1em]
+%
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 2 & 0 \\[-3pt]
+                -1 & 2 & 2 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 2 & 0 \\[-3pt]
+                -1 & 2 & 2 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & \!-1 & 2 & 0 \\[-3pt]
+                -1 & \!-1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 2 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 2 & 0 \\[-3pt]
+                -1 & 2 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 2 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 2 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            & 2
+            \\[1em]
+%
+            & &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & \!-1 & 3 & 0 \\[-3pt]
+                -1 & \!-1 & 2 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 2 & 2 & 0 \\[-3pt]
+                -1 & 3 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 2 & 2 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & \!-1 & 3 & 0 \\[-3pt]
+                -1 & \!-1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 2 & 2 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 2 & 2 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            & 3
+            \\[1em]
+%
+            & & &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 2 & 2 & 0 \\[-3pt]
+                -1 & 3 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 2 & 2 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & \!-1 & 2 & 0 \\[-3pt]
+                -1 & \!-1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 2 & 2 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 2 & 2 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            & 4
+            \\[1em]
+%
+            & & & &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 1 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 1 & 0 \\[-3pt]
+                -1 & 2 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 1 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 3 & 1 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            & 5
+            \\[1em]
+%
+            & & & & &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 1 & 1 & 0 \\[-3pt]
+                -1 & 2 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & \!-1 & 3 & 0 \\[-3pt]
+                -1 & \!-1 & 2 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & \!-1 & 3 & 0 \\[-3pt]
+                -1 & \!-1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            & 6
+            \\[1em]
+%
+            & & & & & &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 2 & 1 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & 2 & 1 & 0 \\[-3pt]
+                -1 & 1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            & 7
+            \\[1em]
+%
+            & & & & & & &
+                \begin{tabular}{|cccc|}
+                \hline
+                -1 & \!-1 & 2 & 0 \\[-3pt]
+                -1 & \!-1 & 1 & 0 \\
+                \hline
+                \end{tabular}
+            & 8
+        \end{tabular}
+    \end{aligned}$
+    };
+\end{scope}
+
+\end{tikzpicture}
+
+\end{document}
+

diff --git a/re2c/doc/tdfa_v2/part_1_tnfa.tex b/re2c/doc/tdfa_v2/part_1_tnfa.tex
index 3bbf0ad1836239835653bea8033cbf645f9d952e..b1df341d1b7b822fecafc61c397ec25896858495 100644 (file)
--- a/re2c/doc/tdfa_v2/part_1_tnfa.tex
+++ b/re2c/doc/tdfa_v2/part_1_tnfa.tex
@@ -730,6 +730,17 @@ $\beta \sim \gamma$ and $\beta \subset \gamma$,
 because $first (\beta \backslash \gamma) = \Xr < \Xl = first (\gamma \backslash \beta)$.
 Therefore $\alpha < \beta < \gamma$.
 }
+\end{figure}
+
+\begin{figure}\label{fig_pe2}
+\includegraphics[width=\linewidth]{img/pe2.pdf}
+\caption{
+An example of PEs for IPTs from figure \ref{fig_mark_enum} and the computation of $traces$ for each pair of PEs.\\
+Here $\alpha \sqsubset \beta$ and $\alpha \sqsubset \gamma$, while
+$\beta \sim \gamma$ and $\beta \subset \gamma$,
+because $first (\beta \backslash \gamma) = \Xr < \Xl = first (\gamma \backslash \beta)$.
+Therefore $\alpha < \beta < \gamma$.
+}
 \end{figure}
 
     \begin{Xdef}\label{prec1}