No Variable is an Island: Computational Complexity and Island Constraints

What constitutes knowledge of language? On one view, it is our ability to pair sound and meaning, ultimately, an information-processing task. This chapter explores one part of that task, the computational implications of locality and island constraints. It is part of a more general research program to probe the connections between constraints on representations and constraints on computation (what might be called the computational analysis of strong generative capacity rather than the computational analysis of weak generative capacity that is associated with the complexity of language classes such as context-free languages). The answers that are beginning to emerge are in a certain sense preliminary, but, it appears, broad enough that a general pattern can now be discerned and worthwhile enough to bring many currently known complexity results under a single framework. In so doing, this chapter will try to answer the following questions: What does it mean to be an island, from a computational point of view? How does the notion of an island interact with a key distinction — perhaps the key distinction — in computation, namely the difference between deterministic and nondeterministic processing?