Consider a PCFG with rule/probability pairs: There are two key transitions in the associated LR automaton, which represent shift actions over c and d (we denote LR states by their sets of kernel items and encode these states into stack symbols): Assume a proper assignment of probabilities to the transitions of the LR automaton, i.e., the sum of transition probabilities for a given LR state is 1.
a probabilistic parsing strategy is defined to be a function S that maps a reduced, proper and consistent PCFG (G, p G ) to a triple S(G, p G ) = (a, p a , f ), where (a, p a ) is a reduced, proper and consistent PPDT, with the same properties as a (non-probabilistic) parsing strategy, and in addition: • For each complete derivation d and each complete computation c such that a complete computation has the same probability as the complete derivation that it is mapped to by function f .