An Automata-Theoretic Approach to Minimalism

Vijay-Shanker et al. (1987) note that many interesting linguistic formalisms can be thought of as having essentially context-free structure, but operating over objects richer than simple strings (sequences of strings, trees, or graphs). They introduce linear context-free rewriting systems (LCFRS’s, see also Weir (1988)) as a unifying framework for superficially different such formalisms (like (multi component) tree adjoining grammars, head grammars, and categorial grammars). Later work (Michaelis, 1998) has added minimalist grammars (MGs, see (Stabler, 1997)) to this list. Recently, Fülöp et al. (2004) have introduced multiple bottom-up tree transducers (mbutt), which can be thought of as offering a transductive perspective on LCFRSs. The transductive perspective allows us to view a grammar in one of these grammar formalisms as defining both a set of well-formed derivations, and functions which interpret these derivations as the derived structures (trees, strings, or meanings) they are derivations of. Being explicit about the structure of the derivation, and divorcing it from the construction of the object so derived has two main advantages. First, we may entertain and study the effects of modifications to the structure of the derivational process, such as insisting that a particular operation apply only in case there is an isomorphic subderivation somewhere in the same derivation (for example, in deletion under identity with an antecedent), or other non-local filters on wellformed derivations, without worrying about the kinds of data structures that would be required to support such operations in real-time (as in parsers, for example). Secondly, viewing derivational grammar formalisms in this way makes particularly salient two loci of language theoretic complexity: