Reword question answering definition

1 files changed, 7 insertions, 6 deletions

diff --git a/mgr.tex b/mgr.tex
index 5f8e6ab..cb631e0 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -330,16 +330,17 @@ MSO to automata direction in this work. See for example Bojańczyk's text
 
 Consider a computational problem whose inputs are of the form $(S, q) \in
 \mathcal{S} \times \mathcal{Q}$ for some set of \definedterm{structures}
-$\mathcal{S}$ and some set of \definedterm{questions} $\mathcal{Q}$. This
-induces a \definedterm{question answering problem} which is divided into two
-phases:
+$\mathcal{S}$ and some set of \definedterm{questions} $\mathcal{Q}$, and answers
+come from a set $\mathcal{A}$. In other words, fix a function $f : \mathcal{S}
+\times \mathcal{Q} \to \mathcal{A}$. This induces a \definedterm{question
+answering problem} which is divided into two phases:
 
 \begin{description}
     \item[preprocessing] An input structure $S \in \mathcal{S}$ is given and a
         \definedterm{preprocessing algorithm} outputs a data structure
-        $S'$.
-    \item[questions] $S'$ is used to handle questions $q_1, \ldots$ from
-        $\mathcal{Q}$.
+        $S'$ (which can be an arbitrary data structure, not necessarily an
+        element of $\mathcal{S}$).
+    \item[questions] Given $S'$ and $q \in \mathcal{Q}$, output $f(S, q)$.
 \end{description}
 
 We are interested in the time complexities of both phases. We use the following