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Precise n-gram Probabilities from Stochastic Context-free Grammars

We present an algorithm for computing n-gram probabilities from stochastic context-free grammars, a procedure that can alleviate some of the standard problems associated with n-grams (estimation from sparse data, lack of linguistic structure, among others). The method operates via the computation of substring expectations, which in turn is accomplished by solving systems of linear equations derived from the grammar. We discuss efficient implementation of the algorithm and report our practical experience with it.