Boolean Functions And Computation Models

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Boolean Functions And Computation Models

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Author : Peter Clote
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-09-19

Boolean Functions And Computation Models written by Peter Clote and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-19 with Computers categories.

The two internationally renowned authors elucidate the structure of "fast" parallel computation. Its complexity is emphasised through a variety of techniques ranging from finite combinatorics, probability theory and finite group theory to finite model theory and proof theory. Non-uniform computation models are studied in the form of Boolean circuits; uniform ones in a variety of forms. Steps in the investigation of non-deterministic polynomial time are surveyed as is the complexity of various proof systems. Providing a survey of research in the field, the book will benefit advanced undergraduates and graduate students as well as researchers.

The Complexity Of Boolean Functions

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Author : Ingo Wegener
language : en
Publisher:
Release Date : 1987

The Complexity Of Boolean Functions written by Ingo Wegener and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.

Boolean Functions And Computation Models

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Author : Peter Clote
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Boolean Functions And Computation Models written by Peter Clote and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Computers categories.

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.

Boolean Models And Methods In Mathematics Computer Science And Engineering

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Author : Yves Crama
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-28

Boolean Models And Methods In Mathematics Computer Science And Engineering written by Yves Crama and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-28 with Computers categories.

A collection of papers written by prominent experts that examine a variety of advanced topics related to Boolean functions and expressions.

Analysis Of Boolean Functions

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Author : Ryan O'Donnell
language : en
Publisher: Cambridge University Press
Release Date : 2014-06-05

Analysis Of Boolean Functions written by Ryan O'Donnell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-05 with Computers categories.

This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.

Boolean Functions

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Author : Yves Crama
language : en
Publisher: Cambridge University Press
Release Date : 2011-05-16

Boolean Functions written by Yves Crama and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-16 with Mathematics categories.

Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics.

Introduction To Circuit Complexity

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Author : Heribert Vollmer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Introduction To Circuit Complexity written by Heribert Vollmer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Computers categories.

An advanced textbook giving a broad, modern view of the computational complexity theory of boolean circuits, with extensive references, for theoretical computer scientists and mathematicians.

Models Of Computation

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Author : Maribel Fernandez
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-14

Models Of Computation written by Maribel Fernandez and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-14 with Computers categories.

A Concise Introduction to Computation Models and Computability Theory provides an introduction to the essential concepts in computability, using several models of computation, from the standard Turing Machines and Recursive Functions, to the modern computation models inspired by quantum physics. An in-depth analysis of the basic concepts underlying each model of computation is provided. Divided into two parts, the first highlights the traditional computation models used in the first studies on computability: - Automata and Turing Machines; - Recursive functions and the Lambda-Calculus; - Logic-based computation models. and the second part covers object-oriented and interaction-based models. There is also a chapter on concurrency, and a final chapter on emergent computation models inspired by quantum mechanics. At the end of each chapter there is a discussion on the use of computation models in the design of programming languages.

Boolean Functions For Cryptography And Coding Theory

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Author : Claude Carlet
language : en
Publisher: Cambridge University Press
Release Date : 2021-01-07

Boolean Functions For Cryptography And Coding Theory written by Claude Carlet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-07 with Computers categories.

A complete, accessible book on single and multiple output Boolean functions in cryptography and coding, with recent applications and problems.

Branching Programs And Binary Decision Diagrams

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Author : Ingo Wegener
language : en
Publisher: SIAM
Release Date : 2000-01-01

Branching Programs And Binary Decision Diagrams written by Ingo Wegener and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.

Finite functions (in particular, Boolean functions) play a fundamental role in computer science and discrete mathematics. This book describes representations of Boolean functions that have small size for many important functions and which allow efficient work with the represented functions. The representation size of important and selected functions is estimated, upper and lower bound techniques are studied, efficient algorithms for operations on these representations are presented, and the limits of those techniques are considered. This book is the first comprehensive description of theory and applications. Research areas like complexity theory, efficient algorithms, data structures, and discrete mathematics will benefit from the theory described in this book. The results described within have applications in verification, computer-aided design, model checking, and discrete mathematics. This is the only book to investigate the representation size of Boolean functions and efficient algorithms on these representations.