Proceedings of Symposia in Applied Mathematics 1989; 128 pp; softcover Volume: 38 Reprint/Revision History: reprinted 1990 ISBN10: 0821801317 ISBN13: 9780821801314 List Price: US$50 Member Price: US$40 Order Code: PSAPM/38
 Computational complexity theory is the study of the quantitative laws that govern computing. During the last 25 years, this field has grown into a rich mathematical theory. Currently one of the most active research areas in computer science, complexity theory is of considerable interest to mathematicians as well, since some of the key open problems in this field raise basic questions about the nature of mathematics. Many experts in complexity theory believe that, in coming decades, the strongest influence on the development of mathematics will come from the extended use of computing and from concepts and problems arising in computer science. This volume contains the proceedings of the AMS Short Course on Computational Complexity Theory, held at the Joint Mathematics Meetings in Atlanta in January 1988. The purpose of the short course was to provide an overview of complexity theory and to describe some of the current developments in the field. The papers presented here represent contributions by some of the top experts in this burgeoning area of research. Readership Table of Contents  J. Hartmanis  Overview of computational complexity theory
 S. R. Mahaney  The isomorphism conjecture and sparse sets
 R. V. Book  Restricted relativizations of complexity classes
 N. Immerman  Descriptive and computational complexity
 A. L. Selman  Complexity issues in cryptography
 S. Goldwasser  Interactive proof systems
