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@@ -531,7 +531,7 @@ labeled with letter $a$ and let $y$ be its parent (or the new vertex
$\mathsf{root}$ when $x$ is the root of $T$). If $A$ in state $q$, reading
letter $a$ goes to $q'$, then there will be an edge from $y.q$ to $x.q'$. In the
word case we had placed copies of $Q$ around each letter and replaced the
-letters with edges implied by $A$'s transition function, here we performed an
+letters with edges implied by $A$'s transition function, here we perform an
analogous transformation on a tree shaped input.
We also color all vertices with colors $1, \ldots, |Q|$ in this graph,