Generative Capacity and Parsing Complexity

Abstract

In this chapter, we complete our study of regular dependency languages by investigating their string-generative capacity and parsing complexity. Specifically, we study the connection between these two measures and the structural constraints discussed in the first part of this book.

We start by explaining how regular dependency grammars can be extended to generators of sets of strings (Section 8.1). We then show that, for the string languages generated by these extended grammars, the block-degree measure induces an infinite hierarchy of expressiveness, and that the well-nestedness restriction properly decreases expressiveness on nearly all levels of this hierarchy (Section 8.2). Finally, we discuss the complexity of the parsing problem of the string languages generated by regular dependency grammars. In particular, we show that the well-nestedness condition can make the change between tractable and intractable parsing (Section 8.3).