Since the early Sixties and Seventies it has been known that the regular and context-free languages are characterized by definability in the monadic second-order theory of certain structures. More recently, these descriptive characterizations have been used to obtain complexity results for constraint- and principle-based theories of syntax and to provide a uniform model-theoretic framework for exploring the relationship between theories expressed in disparate formal terms. These results have been limited, to an extent, by the lack of descriptive characterizations of language classes beyond the context-free. .
