Notes on the Complexity of Complex Heads in a Minimalist Grammar

The type of a minimalist grammar (MG) introduced in Stabler 1997 provides a simple algebraic formalization of the perspectives as they arise from Chomsky 1995b within the linguistic framework of transformational grammar. As known (cf. Michaelis 2001a, 2001b, Harkema 2001), this MG–type defines the same class of derivable string languages as, e.g., linear context–free (string) rewriting systems (Vijay–Shanker et al. 1987, Weir 1988). In this paper we show that, in terms of weak equivalence, the subclass of MGs which allow (overt) head movement but no phrasal movement in the sense of Stabler 1997, constitutes a proper subclass of linear indexed grammars (LIGs), and thus tree adjoining grammars. We also examine the “inner hierarchic complexity” of this embedding in some more detail by looking at the subclasses canonically resulting from the distinction between left and right adjunction of the moved head to the attracting one. Furthermore, we show that adding the possibility of phrasal movement by allowing at most one “indistinguishable” licensee to trigger such movement already increases the weak generative capacity of at least two of the considered subclasses, while this is not true for the particular subclass of MGs which do not employ any movement at all. The latter define the same class of derivable string languages as context free grammars. On the other hand however, MGs which do not employ head movement but whose licensee set consists of at most two elements, are shown to derive, i.a., languages not derivable by any LIG. In this sense our results contribute to shedding some light on the complexity as it arises from the interplay of two different structural transformation types whose common existence is often argued to be linguistically motivated. ∗This work has been funded by DFG–grant STA 519/1–1. A previous version was published in Proceedings of the Sixth International Workshop on Tree Adjoining Grammar and Related Frameworks (TAG+6), pp. 57–65, Universitá di Venezia.