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===Parsing weighted context-free grammars===
It is also possible to extend the CYK algorithm to parse strings using [[weighted context-free grammar|weighted]] and [[stochastic context-free grammar]]s. Weights (probabilities) are then stored in the table P instead of booleans, so P[i,j,A] will contain the minimum weight (maximum probability) that the substring from i to j can be derived from A. Further extensions of the algorithm allow all parses of a string to be enumerated from lowest to highest weight (highest to lowest probability).
==== Numerical stability ====
When the probabilistic CYK algorithm is applied to a long string, the splitting probability can become very small due to multiplying many probabilities together. This can be dealt with by summing log-probability instead of multiplying probabilities.
===Valiant's algorithm===
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