Categorial dependency grammars

Categorial Dependency Grammars (CDGs) are classical categorial grammars extended by oriented polarized valencies. At the same time, CDGs represent a class of completely lexicalized dependency grammars. They express both projective and non-projective dependencies. CDGs generate non-context-free languages. At that, they are parsed in polynomial time under realistic conditions. CDGs possess a normal form that is analogous to Greibach normal form for cf-grammars. CDG-languages are closed under almost all AFL operations and are accepted by a special class of push-down automata with independent counters.