From dc2f73c8bc5827651fa0a3ff5e73cfdf9c38c557 Mon Sep 17 00:00:00 2001
From: Atri Rudra <atri@buffalo.edu>
Date: Mon, 20 Sep 2021 18:07:05 -0400
Subject: [PATCH] Done with pass on S3

---
 mult_distinct_p.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/mult_distinct_p.tex b/mult_distinct_p.tex
index 9ddef5b..30c3ed0 100644
--- a/mult_distinct_p.tex
+++ b/mult_distinct_p.tex
@@ -4,9 +4,9 @@
 \label{sec:hard}
 
 In this section, we will prove the hardness results claimed in Table~\ref{tab:lbs} for a specific (family) of hard instance $(\query,\pdb)$ for \Cref{prob:bag-pdb-poly-expected} where $\pdb$ is a \abbrTIDB.
- Note that this implies hardness for \bis and general \abbrBPDB, answering \Cref{prob:bag-pdb-poly-expected} 
+ Note that this implies hardness for \bis and general \abbrBPDB, showing \Cref{prob:bag-pdb-poly-expected} cannot be done in $O\inparen{\qruntime{\query,\dbbase}}$ runtime.
 %(and hence the equivalent \Cref{prob:bag-pdb-query-eval})
- in the negative. 
+ %in the negative. 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \subsection{Preliminaries}\label{sec:hard:sub:pre}
 Our hardness results are based on (exactly) counting the number of (not necessarily induced) subgraphs in $G$ isomorphic to $H$. Let $\numocc{G}{H}$ denote this quantity.  We can think of $H$ as being of constant size and $G$ as growing.