From a70e6fa206e25f2e177b47b9053a0a3d57970049 Mon Sep 17 00:00:00 2001
From: Marcin Chrzanowski <mc370754@students.mimuw.edu.pl>
Date: Sat, 11 Dec 2021 16:45:10 +0100
Subject: Add tree figure

---
 mgr.tex | 26 ++++++++++++++++++++++++++
 1 file changed, 26 insertions(+)

(limited to 'mgr.tex')

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
-- 
cgit v1.2.3

