Obviously, it needs exponential time to compute the above fractional counts.
due to the property of forest that compactly represents all the parse trees, the posterior probability of a subtree in a forest, | , , can be easily computed in an Inside-Outside fashion as the product of three parts: the outside probability of its root node, the probabilities of parse hyperedges involved in the subtree, and the inside probabilities of its leaf nodes (Lari and Young, 1990;Mi and Huang, 2008).