A Descriptive Approach to Language-Theoretic Complexity

Early formal specifications of natural language syntax were quite closely connected to the notion of abstract machines for computing them. This provided a very natural means of gauging the relative difficulty of processing various constructions, as well as offering some insight into the abstract properties of the human language faculty. More recently, this approach has been superseded by one in which languages are specified in terms of systems of constraints on the structure of their sentences. This has made complexity results difficult to obtain. This book introduces a way of obtaining such results. It presents a natural and quite general means of expressing constraints on the structure of trees and shows that the languages that can be specified by systems of such constraints are exactly those computable by a particular standard class of abstract machines. Thus the difficulty of processing a construction can be reduced to the difficulty of expressing the constraints that specify it. The technique is demonstrated by applying it to a fairly complete treatment of English within the framework of Government and Binding theory, with the result of showing that its complexity is much less than has heretofore been assumed.