  The equivalence problem for unambiguous grammars is an important, but very
difficult open question in formal language theory. Consider the \emph{limited}
equivalence problem for unambiguous grammars -- for two unambiguous grammars
$G_1$ and $G_2$, tell whether or not they describe the same set of words of
length $n$. Obviously, the naive approach requires exponential time with
respect to $n$. By combining two classic algorithmic ideas, I introduce a
$O({\rm poly}(n, |G_1|, |G_2|))$ algorithm for this problem. Moreover, the
ideas behind the algorithm prove useful in various other scenarious.
