Controlled hybrid CD grammar systems

We study the generative power of hybrid CD grammar systems whose derivations are controlled by a graph, a hypothesis language or a generalized sequential machine. We relate them to the families of languages generated by matrix grammars with appearance checking. We thus characterise language families that lie in between that of the families of context-free and context-sensitive languages, which are of particular interest to linguists. In particular, we show that controlled hybrid CD grammar systems can generate the non-context-free features multiple agreements, crossed agreements and (re)duplication that occur in many natural languages.