... first O(n 4) results for the natural formalism of bilexical context-free grammar, and for AI- shawi's (1996) head automaton grammars. For the usual case, split head automaton grammars ... after all: • For bilexicalized context-free grammars, O(n 4) is possible. • The O(n 4) result also holds for head au- tomaton grammars. • For a very common special case of these grammars where ... non-lexicalized CFG. 4 Bilexical CFG in time O(n 4) In this section we give a recognition algorithm for bilexical CNF context-free grammars, which runs in time O(n 4. max(p, IVDI2)) = O(n 4. IVDI3)....