Contributions to the theory of finite-state based grammars

TLDR: It is argued that the findings of this dissertation help to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing.

Abstract: This dissertation is a theoretical study of finite-state based grammars used in natural language processing. The study is concerned with certain varieties of finite-state intersection grammars (FSIGs) whose parsers define regular relations between surface strings and annotated surface strings. The study focuses on the following three aspects of FSIGs: (i) Computational complexity of grammars under limiting parameters In the study, the computational complexity in practical natural language processing is approached through performance-motivated parameters on structural complexity. Each parameter splits some grammars in the Chomsky hierarchy into an infinite set of subset approximations. When the approximations are regular, they seem to fall into the logarithmic-time hierarchy and the dot-depth hierarchy of star-free regular languages. This theoretical result is important and possibly relevant to grammar induction. (ii) Linguistically applicable structural representations Related to the linguistically applicable representations of syntactic entities, the study contains new bracketing schemes that cope with dependency links, leftand right branching, crossing dependencies and spurious ambiguity. New grammar representations that resemble the ChomskySchutzenberger representation of context-free languages are presented in the study, and they include, in particular, representations for mildly context-sensitive non-projective dependency grammars whose performance motivated approximations are linear-time parseable. (iii) Compilation and simplification of linguistic constraints Efficient compilation methods for certain regular operations such as the generalized restriction are presented. These include an elegant algorithm that has already been adopted as the approach in a proprietary finite-state tool. In addition to the compilation methods, an approach to on-the-fly simplifications of finite state representations for parse forests is sketched. These findings are tightly coupled with each other under the theme of locality. I argue that the findings help us to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing.