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The equivalence problem for unambiguous grammars is an important, but verydifficult 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 oflength $n$. Obviously, the naive approach requires exponential time withrespect to $n$. By combining two classic algorithmic ideas, I introduce a$O({\rm poly}(n, |G_1|, |G_2|))$ algorithm for this problem. Moreover, theideas behind the algorithm prove useful in various other scenarious.

Cocke--Younger--Kasami--Schwartz--Zippel algorithm and relatives