Randomness and Completeness in Computational Complexity

  • Dieter van Melkebeek

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1950)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Dieter van Melkebeek
    Pages 1-11
  3. Dieter van Melkebeek
    Pages 13-52
  4. Dieter van Melkebeek
    Pages 53-76
  5. Dieter van Melkebeek
    Pages 77-112
  6. Dieter van Melkebeek
    Pages 113-140
  7. Dieter van Melkebeek
    Pages 141-144
  8. Dieter van Melkebeek
    Pages 145-159
  9. Dieter van Melkebeek
    Pages 161-181
  10. Back Matter
    Pages 183-196

About this book

Introduction

This book contains a revised version of the dissertation the author wrote at the Department of Computer Science of the University of Chicago. The thesis was submitted to the Faculty of Physical Sciences in conformity with the requirements for the PhD degree in June 1999. It was honored with the 1999 ACM Doctoral Dissertation Award in May 2000. Summary Computational complexity is the study of the inherent di culty of compu- tional problems and the power of the tools we may use to solve them. It aims to describe how many resources we need to compute the solution as a function of the problem size. Typical resources include time on sequential and parallel architectures and memory space. As we want to abstract away from details of input representation and speci cs of the computer model, we end up with classes of problems that we can solve within certain robust resource bounds such as polynomial time, parallel logarithmic time, and logarithmic space. Research in complexity theory boils down to determining the relationships between these classes { inclusions and separations. In this dissertation, we focus on the role of randomness and look at various properties of hard problems in order to obtain separations. We also investigate the power of nondeterminism and alternation, as well as space versus time issues. Randomness provides a resource that seems to help in various situations.

Keywords

Algorithms Complete Languages Completeness Complexity Theory Computational Complexity Formal Language Theory Game Theory Randomness Theoretical Computer Science complexity verification

Authors and affiliations

  • Dieter van Melkebeek
    • 1
  1. 1.Institute for Advanced Studies Einstein Drive, PrincetonNJUSA

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-44545-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-41492-6
  • Online ISBN 978-3-540-44545-6
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349
  • About this book