A Weighted Context Free Grammar (WCFG) over Σ with n states is a tuple G = α , {β σ }, A with: where the inside function We will define the outside function α G : Σ × Σ → R n as: For x, z ∈ Σ and y ∈ Σ + we have that is the weight that the grammar assigns to the string xyz with a cut around y.
g Let us make clear that a WCFG is the same device in classic or algebraic forms.