Grammars with Composite Storages

Linear Indexed Grammars (LIGs) can be used to describe nonlocal dependencies. The indexing mechanism however can only account for dependencies that are nested. In natural languages one can easily nd examples in which this simple model cannot be applied straightforwardly. In this paper I will show that a formalism tting better to linguistic structures can be obtained by using a sequence of pushdowns instead of one pushdown for the storage of the indices in a derivation. Crucially, we have to avoid unwanted interactions between the push-downs that would make possible the simulation of a turing machine. 1] solves this problem for multiipushdown automata by restricting reading to the rst nonempty pushdown. I will argue that the corresponding restriction on writing is more natural from a linguistic point of view. I will show that, under each of both restrictions, grammars with a sequence of n pushdowns give rise to a subclass of the nth member of the hierarchy deened by 15, 16], and therefore are mildly context sensitive.