Second-Order Abstract Categorial Grammars as Hyperedge Replacement Grammars

Second-order abstract categorial grammars (de Groote 2001) and hyperedge replacement grammars (see Engelfriet 1997) are two natural ways of generalizing “context-free” grammar formalisms for string and tree languages. It is known that the string generating power of both formalisms is equivalent to (non-erasing) multiple context-free grammars (Seki et al. 1991) or linear context-free rewriting systems (Weir 1988). In this paper, we give a simple, direct proof of the fact that second-order ACGs are simulated by hyperedge replacement grammars, which implies that the string and tree generating power of the former is included in that of the latter. The normal form for tree-generating hyperedge replacement grammars given by Engelfriet and Maneth (2000) can then be used to show that the tree generating power of second-order ACGs is exactly the same as that of hyperedge replacement grammars.