Locality Conditions and the Complexity of Minimalist Grammars: A Preliminary Survey

Among the well-established variety of formal grammar types providing a mildly context-sensitive grammar (MCSG) formalism in the sense of Joshi (1985), Stabler’s minimalist grammars (MGs) (Stabler 1997, 1999) come closest to modeling the tools used in the Chomskyan branch of generative syntax known as “minimalism” (Chomsky 1995, 2000, 2001). Interestingly, without there being a rise in (at least weak) generative power, (extensions and variants of) MGs accommodate a wide variety of (arguably) “odd” items from the syntactician’s toolbox, such as head movement (Stabler 1997, 2001), affix hopping (Stabler 2001), (strict) remnant movement (Stabler 1997, 1999), and (to some extent) adjunction and scrambling (Frey and Gärtner 2002; Gärtner and Michaelis 2003). As a descendant of transformational grammar (TG), minimalism carries over the division of labor between a phrase-structural and a transformational component. These find their way into MGs as operations merge and move, respectively. As is well-known, the Aspects-vintage of TG (Chomsky 1965) was shown to be Turing equivalent by Peters and Ritchie 1973. This led to intensive investigation into locality conditions (LCs) (Chomsky 1973, 1977, 1986; Rizzi 1990; Cinque 1990; Manzini 1992; among others) in an attempt to restrict the power of transformations. However, complexity results for these grammars with LC-add-ons are largely absent.1 This picture has changed with MGs, as a formalized version of minimalism, which were shown to belong among