A Tree Transducer Model of Reference-Set Computation

Reference-set constraints are a special class of constraints used in Minimalist syntax. They extend the notion of well-formedness beyond the level of single trees: When presented with some phrase structure tree, they compute its set of competing output candidates and determine the optimal output(s) according to some economy metric. Doubts have frequently been raised in the literature whether such constraints are computationally tractable (Johnson and Lappin 1999). I define a subclass of Optimality Systems (OSs) that is sufficiently powerful to accommodate a wide range of reference-set constraints and show that these OSs are globally optimal in the sense of Jäger (2002), a prerequisite for them being computable by linear tree transducers. As regular and linear context-free tree languages are closed under linear tree transductions, this marks an important step towards showing that the expressivity of various syntactic formalisms is not increased by adding reference-set constraints. In the second half of the paper, I demonstrate the feasibility of the OS-based transducer approach by exhibiting the transducers for three prominent reference-set constraints, Focus Economy (Reinhart 2006), Merge-over-Move (Chomsky 1995b), and Fewest Steps (Chomsky 1991, 1995b). My approach sheds new light on the internal mechanics of these constraints and suggests that their advantages over standard well-formedness conditions have not been sufficiently exploited in the empirical literature.