A nontechnical introduction to complexity theory: its strengths, its weaknesses, and how it can be used to study grammars.

Ever since Chomsky laid the framework for a mathematically formal theory of syntax, two classes of formal models have held wide appeal. The finite state model offered simplicity. At the opposite extreme numerous very powerful models, most notable transformational grammar, offered generality. As soon as this mathematical framework was laid, devastating arguments were given by Chomsky and others indicating that the finite state model was woefully inadequate for the syntax of natural language. In response, the completely general transformational grammar model was advanced as a suitable vehicle for capturing the description of natural language syntax. While transformational grammar seems likely to be adequate to the task, many researchers have advanced the argument that it is "too adequate. " A now classic result of Peters and Ritchie shows that the model of transformational grammar given in Chomsky's Aspects [IJ is powerful indeed. So powerful as to allow it to describe any recursively enumerable set. In other words it can describe the syntax of any language that is describable by any algorithmic process whatsoever. This situation led many researchers to reasses the claim that natural languages are included in the class of transformational grammar languages. The conclu sion that many reached is that the claim is void of content, since, in their view, it says little more than that natural language syntax is doable algo rithmically and, in the framework of modern linguistics, psychology or neuroscience, that is axiomatic.

This comprehensive reference work provides an overview of the concepts, methodologies, and applications in computational linguistics and natural language processing (NLP). Features contributions by the top researchers in the field, reflecting the work that is driving the discipline forward Includes an introduction to the major theoretical issues in these fields, as well as the central engineering applications that the work has produced Presents the major developments in an accessible way, explaining the close connection between scientific understanding of the computational properties of natural language and the creation of effective language technologies Serves as an invaluable state-of-the-art reference source for computational linguists and software engineers developing NLP applications in industrial research and development labs of software companies

The central task of future-oriented computational linguistics is the development of cognitive machines which humans can freely speak to in their natural language. This will involve the development of a functional theory of language, an objective method of verification, and a wide range of practical applications. Natural communication requires not only verbal processing, but also non-verbal perception and action. Therefore, the content of this book is organized as a theory of language for the construction of talking robots with a focus on the mechanics of natural language communication in both the listener and the speaker.

This work elucidates the structure and complexity of human language in terms of the mathematics of information and computation. It strengthens Chomsky's early work on the mathematics of language, with the advantages of a better understanding of language and a more precise theory of structural complexity. Ristad argues that language is the process of constructing linguistic representations from the forms produced by other cognitive modules and that this process is NP-complete. This NP-completeness is defended with a phalanx of elegant and revealing proofs that rely only on the empirical facts of linguistic knowledge and on the uncontroverted assumption that these facts generalize in a reasonable manner. For this reason, these complexity results apply to all adequate linguistic theories and are the first to do so. Eric Sven Ristad is Assistant Professor of Computer Science at Princeton University. He is the coauthor of Computational Complexity and Natural Language. Contents:Foundation of the Investigation. Anaphora. Ellipsis. Phonology. Syntactic Agreement and Lexical Ambiguity. Philosophical Issues.

We also give algorithms for learning powerful concept classes under the uniform distribution, and give equivalences between natural models of efficient learnability. This thesis also includes detailed definitions and motivation for the distribution-free model, a chapter discussing past research in this model and related models, and a short list of important open problems."

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.