Done with pass on S3

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.