Add tree figure

5 files changed, 142 insertions, 0 deletions

diff --git a/mgr.tex b/mgr.tex
index ce27d02..a89eb4b 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -5,6 +5,7 @@
 \usepackage{definitions}
 \usepackage[backend=biber]{biblatex}
 \usepackage{graphicx}
+\usepackage{subcaption}
 \addbibresource{mgr.bib}
 
 \usepackage{amsmath}
@@ -543,6 +544,31 @@ This process will again lead to a coloring with the desired properties that
         child copy of $Q$, then $c \geq c'$.
 \end{enumerate}
 
+\begin{figure}
+    \centering
+    \def\svgwidth{\columnwidth}
+    \begin{subfigure}{0.3\linewidth}
+        \input{tree.pdf_tex}
+        \caption{The original tree $T$}
+    \end{subfigure}
+    \def\svgwidth{\columnwidth}
+    \begin{subfigure}{0.4\linewidth}
+        \input{tree-graph.pdf_tex}
+        \caption{The colored graph}
+    \end{subfigure}
+    \caption{
+        On the left, a sample labeled tree. On the right, the colored graph we
+        create for the purposes of answering branch infix regular questions for
+        this tree and a simple three state automaton. Note how the copies of the
+        automaton's states are arranged in the same as shape as $T$, with an
+        additional new root copy. The letters of the original tree fit in the
+        spaces between copies of $Q$, inducing the edges between them.
+    }\label{tree-figure}
+\end{figure}
+
+See Figure \ref{tree-figure} for how the colored graph is constructed for an
+example tree.
+
 Now let's consider how we could answer the question ``is the branch infix from
 $x$ down to $y$ in $L$?''. Here we can't proceed exactly as in the word case. We
 don't have a $\breaktable$ table since a vertex in an internal node can have
diff --git a/tree-graph.pdf b/tree-graph.pdf
new file mode 100644
index 0000000..d0723c8
--- /dev/null
+++ b/tree-graph.pdf
diff --git a/tree-graph.pdf_tex b/tree-graph.pdf_tex
new file mode 100644
index 0000000..998c358
--- /dev/null
+++ b/tree-graph.pdf_tex
@@ -0,0 +1,58 @@
+%% Creator: Inkscape 1.1.1 (3bf5ae0d25, 2021-09-20, custom), www.inkscape.org
+%% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010
+%% Accompanies image file 'tree-graph.pdf' (pdf, eps, ps)
+%%
+%% To include the image in your LaTeX document, write
+%%   \input{<filename>.pdf_tex}
+%%  instead of
+%%   \includegraphics{<filename>.pdf}
+%% To scale the image, write
+%%   \def\svgwidth{<desired width>}
+%%   \input{<filename>.pdf_tex}
+%%  instead of
+%%   \includegraphics[width=<desired width>]{<filename>.pdf}
+%%
+%% Images with a different path to the parent latex file can
+%% be accessed with the `import' package (which may need to be
+%% installed) using
+%%   \usepackage{import}
+%% in the preamble, and then including the image with
+%%   \import{<path to file>}{<filename>.pdf_tex}
+%% Alternatively, one can specify
+%%   \graphicspath{{<path to file>/}}
+%% 
+%% For more information, please see info/svg-inkscape on CTAN:
+%%   http://tug.ctan.org/tex-archive/info/svg-inkscape
+%%
+\begingroup%
+  \makeatletter%
+  \providecommand\color[2][]{%
+    \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}%
+    \renewcommand\color[2][]{}%
+  }%
+  \providecommand\transparent[1]{%
+    \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}%
+    \renewcommand\transparent[1]{}%
+  }%
+  \providecommand\rotatebox[2]{#2}%
+  \newcommand*\fsize{\dimexpr\f@size pt\relax}%
+  \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}%
+  \ifx\svgwidth\undefined%
+    \setlength{\unitlength}{1372.34923535bp}%
+    \ifx\svgscale\undefined%
+      \relax%
+    \else%
+      \setlength{\unitlength}{\unitlength * \real{\svgscale}}%
+    \fi%
+  \else%
+    \setlength{\unitlength}{\svgwidth}%
+  \fi%
+  \global\let\svgwidth\undefined%
+  \global\let\svgscale\undefined%
+  \makeatother%
+  \begin{picture}(1,0.90071325)%
+    \lineheight{1}%
+    \setlength\tabcolsep{0pt}%
+    \put(0,0){\includegraphics[width=\unitlength,page=1]{tree-graph.pdf}}%
+  \end{picture}%
+\endgroup%
diff --git a/tree.pdf b/tree.pdf
new file mode 100644
index 0000000..d4da0aa
--- /dev/null
+++ b/tree.pdf
diff --git a/tree.pdf_tex b/tree.pdf_tex
new file mode 100644
index 0000000..36d98d1
--- /dev/null
+++ b/tree.pdf_tex
@@ -0,0 +1,58 @@
+%% Creator: Inkscape 1.1.1 (3bf5ae0d25, 2021-09-20, custom), www.inkscape.org
+%% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010
+%% Accompanies image file 'tree.pdf' (pdf, eps, ps)
+%%
+%% To include the image in your LaTeX document, write
+%%   \input{<filename>.pdf_tex}
+%%  instead of
+%%   \includegraphics{<filename>.pdf}
+%% To scale the image, write
+%%   \def\svgwidth{<desired width>}
+%%   \input{<filename>.pdf_tex}
+%%  instead of
+%%   \includegraphics[width=<desired width>]{<filename>.pdf}
+%%
+%% Images with a different path to the parent latex file can
+%% be accessed with the `import' package (which may need to be
+%% installed) using
+%%   \usepackage{import}
+%% in the preamble, and then including the image with
+%%   \import{<path to file>}{<filename>.pdf_tex}
+%% Alternatively, one can specify
+%%   \graphicspath{{<path to file>/}}
+%% 
+%% For more information, please see info/svg-inkscape on CTAN:
+%%   http://tug.ctan.org/tex-archive/info/svg-inkscape
+%%
+\begingroup%
+  \makeatletter%
+  \providecommand\color[2][]{%
+    \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}%
+    \renewcommand\color[2][]{}%
+  }%
+  \providecommand\transparent[1]{%
+    \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}%
+    \renewcommand\transparent[1]{}%
+  }%
+  \providecommand\rotatebox[2]{#2}%
+  \newcommand*\fsize{\dimexpr\f@size pt\relax}%
+  \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}%
+  \ifx\svgwidth\undefined%
+    \setlength{\unitlength}{567.89071872bp}%
+    \ifx\svgscale\undefined%
+      \relax%
+    \else%
+      \setlength{\unitlength}{\unitlength * \real{\svgscale}}%
+    \fi%
+  \else%
+    \setlength{\unitlength}{\svgwidth}%
+  \fi%
+  \global\let\svgwidth\undefined%
+  \global\let\svgscale\undefined%
+  \makeatother%
+  \begin{picture}(1,1.02815594)%
+    \lineheight{1}%
+    \setlength\tabcolsep{0pt}%
+    \put(0,0){\includegraphics[width=\unitlength,page=1]{tree.pdf}}%
+  \end{picture}%
+\endgroup%