An Earley-Style Parser for Multiple Context-Free Grammars

We de ne an m-multiple context-free grammar (m-mcfg) as in Seki et al. 1991. A multiple context-free grammar G is a ve-tuple 〈N,O,F,R, S〉, where N is a set of distinguished non-terminal symbols; O ⊆ ⋃ n∈N+(Σ ∗)n is a set of tuples of strings from the input alphabet Σ; F ⊆ ⋃ n∈N Fn, where Fn is the set of partial functions from On to O, is a set of string-transformation functions; R ⊆ ⋃ n∈N(N × Nn × (Fn ∩ F )) is a set of grammar rules, written A → g[B1 . . . Bn(g)] for A,Bi ∈ N, 1 ≤ i ≤ n(g), g ∈ Fn(g); and S ∈ N is a distinguished start symbol. To qualify as an m-mcfg, the grammar must further have the following properties: 1. The dimension of tuples in O is bounded: O ⊆ ⋃m i=1(Σ ∗)i 2. For all g ∈ Fn(g),