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  • Textbook
  • © 2012

Boolean Function Complexity

Advances and Frontiers

Authors:

  • This is the first book covering the happening in circuit complexity during the last 20 years

  • Includes non-standard topics, like graph complexity or circuits with arbitrary gates

  • Includes about 40 open problems as potential research topics for students ?

  • Includes supplementary material: sn.pub/extras

Part of the book series: Algorithms and Combinatorics (AC, volume 27)

Buying options

eBook USD 79.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-24508-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 99.99
Price excludes VAT (USA)
Hardcover Book USD 139.99
Price excludes VAT (USA)

This is a preview of subscription content, access via your institution.

Table of contents (20 chapters)

  1. Front Matter

    Pages i-xv
  2. The Basics

    1. Front Matter

      Pages 1-1
    2. Our Adversary: The Circuit

      • Stasys Jukna
      Pages 3-53
    3. Analysis of Boolean Functions

      • Stasys Jukna
      Pages 55-77
  3. Communication Complexity

    1. Front Matter

      Pages 79-79
    2. Games on Relations

      • Stasys Jukna
      Pages 81-92
    3. Games on 0-1 Matrices

      • Stasys Jukna
      Pages 93-134
    4. Multi-Party Games

      • Stasys Jukna
      Pages 135-156
  4. Circuit Complexity

    1. Front Matter

      Pages 157-157
    2. Formulas

      • Stasys Jukna
      Pages 159-203
    3. Monotone Formulas

      • Stasys Jukna
      Pages 205-228
    4. Span Programs

      • Stasys Jukna
      Pages 229-243
    5. Monotone Circuits

      • Stasys Jukna
      Pages 245-284
    6. The Mystery of Negations

      • Stasys Jukna
      Pages 285-300
  5. Bounded Depth Circuits

    1. Front Matter

      Pages 301-301
    2. Depth-3 Circuits

      • Stasys Jukna
      Pages 303-338
    3. Large-Depth Circuits

      • Stasys Jukna
      Pages 339-369
    4. Circuits with Arbitrary Gates

      • Stasys Jukna
      Pages 371-402
  6. Branching Programs

    1. Front Matter

      Pages 403-403
    2. Decision Trees

      • Stasys Jukna
      Pages 405-437

About this book

Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive  description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.

Keywords

  • Boolean functions
  • circuit complexity
  • communication complexity
  • lower bounds
  • information and communication, circuits
  • combinatorics

Reviews

“All material in the book is accessible to graduate or even undergraduate students of computer science, mathematics or electrical engineering. … I gladly recommend this book to beginning students, who will find this book a good starting point in exploring the field of complexity theory, as well as to mature researchers who would like to bring themselves up-to-date on some aspect of the theory. … the book contains a large number of open research problems, including some really enticing ones!” (Sergey Yekhanin, SIAM Review, Vol. 57 (3), September, 2015)

“The results stated in the book are well motivated and given with an intuitive explanation of their proof idea wherever appropriate. … Each chapter of the book contains open research problems and a section with exercises to deepen the understanding of the presented material and make the book suitable for course work. The book is well suited for graduate students and professionals who seek an accessible, research-oriented guide to the important techniques for proving lower bounds on the complexity of problems connected to Boolean functions.” (Michael Thomas, Mathematical Reviews, January, 2013)

“Jukna, a well-known researcher in the field, has succeeded in producing an excellent comprehensive exposition on the field, starting from early results from the '40s and '50s and proceeding to the most recent achievements. … The book is going to be very useful for researchers and graduate students in computer science and discrete mathematics. … The style of writing is pleasant … . The many exercises and research problems round out the highlights of this recommendable book.” (Arto Salomaa, ACM Computing Reviews, June, 2012)

“This monograph is about circuit complexity, dealing with establishing lower bounds on the computational complexity of specific problems … . The book is mainly devoted to mathematicians, to researchers in computer science wishing to complete their knowledge about the state of the art in circuit complexity, as well as to graduate students in mathematics and computer science, and is self-contained. … An impressive work providing a large amount of information on circuit complexity.” (Ioan Tomescu, Zentralblatt MATH, Vol. 1235, 2012)

Authors and Affiliations

  • , Institute of Informatics, University of Frankfurt, Frankfurt, Germany

    Stasys Jukna

About the author

http://www.thi.informatik.uni-frankfurt.de/~jukna/

Bibliographic Information

Buying options

eBook USD 79.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-24508-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 99.99
Price excludes VAT (USA)
Hardcover Book USD 139.99
Price excludes VAT (USA)