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Boolean Functions and Computation Models

  • Textbook
  • © 2002

Overview

Authors:
  1. Peter Clote

    1. Department of Computer Science and Department of Biology, Boston College, Chestnut Hill, USA

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  2. Evangelos Kranakis

    1. School of Computer Science, Carleton University, Ottawa, Canada

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    You can also search for this author in PubMed   Google Scholar

  • A survey of the present state of the art by internationally well-known authors
  • Focus on "fast" parallel computation
  • Includes numerous exercises ranging in difficulty
  • Includes supplementary material: sn.pub/extras

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XIV
    Download chapter PDF

  2. Boolean Functions and Circuits

    • Peter Clote, Evangelos Kranakis
    Pages 1-60

  3. Circuit Lower Bounds

    • Peter Clote, Evangelos Kranakis
    Pages 61-154

  4. Circuit Upper Bounds

    • Peter Clote, Evangelos Kranakis
    Pages 155-205

  5. Randomness and Satisfiability

    • Peter Clote, Evangelos Kranakis
    Pages 207-245

  6. Propositional Proof Systems

    • Peter Clote, Evangelos Kranakis
    Pages 247-412

  7. Machine Models and Function Algebras

    • Peter Clote, Evangelos Kranakis
    Pages 413-495

  8. Higher Types

    • Peter Clote, Evangelos Kranakis
    Pages 497-567

  9. Back Matter

    Pages 569-602
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Keywords

About this book

The foundations of computational complexity theory go back to Alan Thring in the 1930s who was concerned with the existence of automatic procedures deciding the validity of mathematical statements. The first example of such a problem was the undecidability of the Halting Problem which is essentially the question of debugging a computer program: Will a given program eventu­ ally halt? Computational complexity today addresses the quantitative aspects of the solutions obtained: Is the problem to be solved tractable? But how does one measure the intractability of computation? Several ideas were proposed: A. Cobham [Cob65] raised the question of what is the right model in order to measure a "computation step" , M. Rabin [Rab60] proposed the introduction of axioms that a complexity measure should satisfy, and C. Shannon [Sha49] suggested the boolean circuit that computes a boolean function. However, an important question remains: What is the nature of computa­ tion? In 1957, John von Neumann [vN58] wrote in his notes for the Silliman Lectures concerning the nature of computation and the human brain that . . . logics and statistics should be primarily, although not exclusively, viewed as the basic tools of 'information theory'. Also, that body of experience which has grown up around the planning, evaluating, and coding of complicated logical and mathematical automata will be the focus of much of this information theory. The most typical, but not the only, such automata are, of course, the large electronic computing machines.

Reviews

From the reviews:

"The monograph gives the most recent and complete description of lower bounds for depth-restricted circuits, and propositional proof systems. … the authors present a research monograph on important subjects and provide many very recent results. I would recommend it for any university library and also for researchers." (Ingo Wegener, The Computer Journal, Vol. 46 (3), 2003)

Authors and Affiliations

  • Department of Computer Science and Department of Biology, Boston College, Chestnut Hill, USA

    Peter Clote

  • School of Computer Science, Carleton University, Ottawa, Canada

    Evangelos Kranakis

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