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Parameterized Complexity in the Polynomial Hierarchy

Extending Parameterized Complexity Theory to Higher Levels of the Hierarchy

  • RonaldĀ de Haan
Book

Part of the Lecture Notes in Computer Science book series (LNCS, volume 11880)

Also part of the Theoretical Computer Science and General Issues book sub series (LNTCS, volume 11880)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Ronald de Haan
    Pages 1-18
  3. Foundations

    1. Front Matter
      Pages 19-19
    2. Ronald de Haan
      Pages 21-32
    3. Ronald de Haan
      Pages 33-41
  4. Beyond Para-NP

    1. Front Matter
      Pages 43-43
    2. Ronald de Haan
      Pages 45-69
    3. Ronald de Haan
      Pages 71-83
    4. Ronald de Haan
      Pages 85-135
    5. Ronald de Haan
      Pages 137-157
  5. Applying the Theory

    1. Front Matter
      Pages 159-159
    2. Ronald de Haan
      Pages 181-204
    3. Ronald de Haan
      Pages 219-250
    4. Ronald de Haan
      Pages 251-259
    5. Ronald de Haan
      Pages 261-268
  6. Relation to Other Topics in Complexity Theory

    1. Front Matter
      Pages 269-269
    2. Ronald de Haan
      Pages 271-283
    3. Ronald de Haan
      Pages 285-332
  7. Conclusions

    1. Front Matter
      Pages 333-333
    2. Ronald de Haan
      Pages 335-347
    3. Ronald de Haan
      Pages 349-353
  8. Back Matter
    Pages 355-398

About this book

Introduction

The book presents the co-recipient of the E.W. Beth Dissertation Prize 2017 for outstanding dissertations in the fields of logic, language, and information. This work extends the theory of parameterized complexity to higher levels of the Polynomial Hierarchy (PH). For problems at higher levels of the PH, a promising solving approach is to develop fixed-parameter tractable reductions to SAT, and to subsequently use a SAT solving algorithm to solve the problem. In this dissertation, a theoretical toolbox is developed that can be used to classify in which cases this is possible. The use of this toolbox is illustrated by applying it to analyze a wide range of problems from various areas of computer science and artificial intelligence.

Keywords

Computational complexity Parameterized complexity Fixed-parameter tractability Fpt-reductions Polynomial Hierarchy Complexity classes Automated reasoning SAT solving Answer set programming Subexponential-time complexity Temporal logic

Authors and affiliations

  • RonaldĀ de Haan
    • 1
  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-60670-4
  • Copyright Information Springer-Verlag GmbH Germany, part of Springer Nature 2019
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-662-60669-8
  • Online ISBN 978-3-662-60670-4
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349
  • Buy this book on publisher's site