Cocke–Younger–Kasami–Schwartz–Zippel algorithm and relatives
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The equivalence problem for unambiguous grammars is an important, but very difficult open question in formal language theory. Consider the 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( poly(n, |G_1|, |G_2|)) algorithm for this problem. Moreover, the ideas behind the algorithm prove useful in various other scenarious.
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