Overview
- 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
Part of the book series: Texts in Theoretical Computer Science. An EATCS Series (TTCS)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
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.
Similar content being viewed by others
Keywords
Table of contents (7 chapters)
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
Bibliographic Information
Book Title: Boolean Functions and Computation Models
Authors: Peter Clote, Evangelos Kranakis
Series Title: Texts in Theoretical Computer Science. An EATCS Series
DOI: https://doi.org/10.1007/978-3-662-04943-3
Publisher: Springer Berlin, Heidelberg
-
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2002
Hardcover ISBN: 978-3-540-59436-9Published: 19 September 2002
Softcover ISBN: 978-3-642-08217-7Published: 21 October 2010
eBook ISBN: 978-3-662-04943-3Published: 09 March 2013
Series ISSN: 1862-4499
Series E-ISSN: 1862-4502
Edition Number: 1
Number of Pages: XIV, 602
Topics: Computer System Implementation, Computation by Abstract Devices, Mathematical Logic and Formal Languages, Programming Techniques, Mathematical Logic and Foundations