From efe68b7702eee84432158c8065b107046f79354c Mon Sep 17 00:00:00 2001
From: Marcin Chrzanowski <mc370754@students.mimuw.edu.pl>
Date: Fri, 6 Aug 2021 14:29:57 -0400
Subject: Define the branch infix query problem

---
 mgr.tex | 13 ++++++++++++-
 1 file changed, 12 insertions(+), 1 deletion(-)

(limited to 'mgr.tex')

diff --git a/mgr.tex b/mgr.tex
index cf7bb8b..9ac68b0 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -133,7 +133,18 @@ The construction is as follows:
 Additionally, in each vertex, we store the index of the next copy of $Q$ in
 which the path of this vertex's color is broken by a lower color.
 
-\section{Least Common Ancestor via Range Minimum Query}
+\section{Generalizing to trees}
+
+We will now generalize the above construction from regular infix queries on a
+word, to ones on a tree. The exact problem we're solving is
+
+\emph{Given}: a tree $T$ with labels from alphabet $\Sigma$, a deterministic
+finite automaton $A$.
+
+\emph{Queries}: given a vertex $x$ and its descendant $y$, is the word given by
+labels on the path from $x$ to $y$ accepted by $A$?
+
+
 
 \section{Highest Black Descendant on Path}
 
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