We now map (A, p A ) to a language-equivalent PCFG (G , p G ), G = (Σ  , Q, X in , R ), where R contains the following rules with the specified associated probabilities: , for each X → XY ∈ ∆ with Z the unique stack symbol such that there is at least one transition XY → Z with Y ; Y ; • Y → ε with p G (X → ε) = 1, for each stack symbol Y such that there is at least one transition XY → Z ∈ ∆ or such that Y = X f in .
it is not difficult to see that there exists a bijection f from complete computations of A to complete derivations of G , and that we have for each complete computation c. (G , p G ) is consistent.