Boolean Functions

by Yves Crama

The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations.

Boolean Functions

Author: Yves Crama

Publisher: Cambridge University Press

ISBN: 1139498630

Page:

View: 258

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.

Boolean Functions and Computation Models

by Peter Clote

The book will benefit advanced undergraduate and graduate students as well as researchers in the field of complexity theory.

Boolean Functions and Computation Models

Author: Peter Clote

Publisher: Springer Science & Business Media

ISBN: 3662049430

Page: 602

View: 728

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.

Analysis of Boolean Functions

by Ryan O'Donnell

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.

Analysis of Boolean Functions

Author: Ryan O'Donnell

Publisher: Cambridge University Press

ISBN: 1107038324

Page: 444

View: 942

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.

Timed Boolean Functions

by William K.C. Lam

The goal of the book is to present the central idea of representing logical and timing information in a common structure, TBFs, and to present a canonical form suitable for efficient manipulation.

Timed Boolean Functions

Author: William K.C. Lam

Publisher: Springer Science & Business Media

ISBN: 9780792394549

Page: 273

View: 479

Timing research in high performance VLSI systems has advanced at a steady pace over the last few years. Tools, however, especially theoretical mechanisms, lag behind. Much of the present timing research relies heavily on timing diagrams, which although intuitive, are inadequate for analysis of large designs with many parameters. Further, timing diagrams offer only approximations, not exact solutions to many timing problems and provide little insight in the cases where temporal properties of a design interact intricately with the design's logical functionalities. Timed Boolean Functions presents a methodology for timing research which facilitates analysis and design of circuits and systems in a unified temporal and logical domain. The goal of the book is to present the central idea of representing logical and timing information in a common structure, TBFs, and to present a canonical form suitable for efficient manipulation. This methodology is then applied to practical applications to provide intuition and insight into the subject so that these general methods can be adapted to specific engineering problems and also to further the research necessary to enhance the understanding of the field. Timed Boolean Functions is written for professionals involved in timing research and digital designers who want to enhance their understanding of the timing aspects of high speed circuits. The prerequisites are a common background in logic design, computer algorithms, combinatorial optimization and a certain degree of mathematical sophistication.

Canadian Journal of Mathematics

by

BOOLEAN. FUNCTIONS. OF. n. VARIABLES. DAVID SLEPIAN 1. Introduction. In
recent years Boolean Algebra has come to play a prominent role in the analysis
and synthesis of switching circuits [1; 4]. One general synthesis problem in which
 ...

Canadian Journal of Mathematics

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Page: 144

View: 842

Boolean Functions and Their Applications in Cryptography

by Chuan-Kun Wu

This book focuses on the different representations and cryptographic properties of Booleans functions, presents constructions of Boolean functions with some good cryptographic properties.

Boolean Functions and Their Applications in Cryptography

Author: Chuan-Kun Wu

Publisher: Springer

ISBN: 3662488655

Page: 256

View: 429

This book focuses on the different representations and cryptographic properties of Booleans functions, presents constructions of Boolean functions with some good cryptographic properties. More specifically, Walsh spectrum description of the traditional cryptographic properties of Boolean functions, including linear structure, propagation criterion, nonlinearity, and correlation immunity are presented. Constructions of symmetric Boolean functions and of Boolean permutations with good cryptographic properties are specifically studied. This book is not meant to be comprehensive, but with its own focus on some original research of the authors in the past. To be self content, some basic concepts and properties are introduced. This book can serve as a reference for cryptographic algorithm designers, particularly the designers of stream ciphers and of block ciphers, and for academics with interest in the cryptographic properties of Boolean functions.

Cryptographic Boolean Functions and Applications

by Thomas W. Cusick

This book follows the previous edition in sifting through this compendium and gathering the most significant information in one concise reference book.

Cryptographic Boolean Functions and Applications

Author: Thomas W. Cusick

Publisher: Academic Press

ISBN: 0128111305

Page: 288

View: 522

Cryptographic Boolean Functions and Applications, Second Edition is designed to be a comprehensive reference for the use of Boolean functions in modern cryptography. While the vast majority of research on cryptographic Boolean functions has been achieved since the 1970s, when cryptography began to be widely used in everyday transactions, in particular banking, relevant material is scattered over hundreds of journal articles, conference proceedings, books, reports and notes, some of them only available online. This book follows the previous edition in sifting through this compendium and gathering the most significant information in one concise reference book. The work therefore encompasses over 600 citations, covering every aspect of the applications of cryptographic Boolean functions. Since 2008, the subject has seen a very large number of new results, and in response, the authors have prepared a new chapter on special functions. The new edition brings 100 completely new references and an expansion of 50 new pages, along with heavy revision throughout the text. Presents a foundational approach, beginning with the basics of the necessary theory, then progressing to more complex content Includes major concepts that are presented with complete proofs, with an emphasis on how they can be applied Includes an extensive list of references, including 100 new to this edition that were chosen to highlight relevant topics Contains a section on special functions and all-new numerical examples

Boolean Functions

by Serban E. Vlad

This book: Presents up-to-date research in the field of Boolean networks, Includes the information needed to understand the construction of an asynchronous Boolean systems theory and contains proofs, Employs use of the language of algebraic ...

Boolean Functions

Author: Serban E. Vlad

Publisher: Wiley

ISBN: 1119517478

Page: 208

View: 352

The essential guide showing how the unbounded delay model of computation of the Boolean functions may be used in the analysis of the Boolean networks Boolean Functions: Topics in Asynchronicity contains the most current research in several issues of asynchronous Boolean systems. In this framework, asynchronicity means that the functions which model the digital circuits from electronics iterate their coordinates independently on each other and the author—a noted expert in the field—includes a formal mathematical description of these systems. Filled with helpful definitions and illustrative examples, the book covers a range of topics such as morphisms, antimorphisms, invariant sets, path connected sets, attractors. Further, it studies race freedom, called here the technical condition of proper operation, together with some of its generalized and strengthened versions, and also time reversal, borrowed from physics and also from dynamical systems, together with the symmetry that it generates. This book: Presents up-to-date research in the field of Boolean networks, Includes the information needed to understand the construction of an asynchronous Boolean systems theory and contains proofs, Employs use of the language of algebraic topology and homological algebra. Written formathematicians and computer scientists interested in the theory and applications of Boolean functions, dynamical systems, and circuits, Boolean Functions: Topics in Asynchronicity is an authoritative guide indicating a way of using the unbounded delay model of computation of the Boolean functions in the analysis of the Boolean networks.

The Complexity of Boolean Functions

by Ingo Wegener

Ugolnikov ( 76 ) : On the realizations of monotone functions by circuits of
functional elements . Probl . Kibern . 31 , 167 - 185 . ... Wegener ( 81 ) : An
improved complexity hierarchy on the depth of Boolean functions . Acta Inform .
15 , 147 - 152 .

The Complexity of Boolean Functions

Author: Ingo Wegener

Publisher: Wiley

ISBN: 9780471915553

Page: 470

View: 378

Presents a large number of recent research results previously unavailable in book form. Initially deals with the wee-known computation models, and goes on to special types of circuits, parallel computers, and branching programs. Includes basic theory as well recent research findings. Each chapter includes exercises.

Scientific and Technical Aerospace Reports

by

... by using Boolean matrices 02 p0204 N66-11415 Different structures of discrete
functions and their variables Boolean ... minimizing functions of manyvalued logic
from similar technique for Boolean functions 08 p1261 N66-17371 Functions ...

Scientific and Technical Aerospace Reports

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Applied Mechanics Reviews

by

6 ) it follows : if there exists a Boolean function F for which equality ( 1 . 6 ) is true ,
then function s is an R - function . Function F is called an accompanying function
for f . We shall now give concise information about Boolean functions . Boolean ...

Applied Mechanics Reviews

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Fonctions bool ennes Boolean Functions

by Jean-Francis Michon

En mars 2006 s'est tenu à Rouen BFCA'06, le second atelier sur le thème des Fonctions Booléennes. Pendant trois jours, de nombreux chercheurs internationaux s'y sont rencontrés et y ont parlé de leurs travaux.

Fonctions bool ennes Boolean Functions

Author: Jean-Francis Michon

Publisher: Publication Univ Rouen Havre

ISBN: 9782877754224

Page: 201

View: 708

En mars 2006 s'est tenu à Rouen BFCA'06, le second atelier sur le thème des Fonctions Booléennes. Pendant trois jours, de nombreux chercheurs internationaux s'y sont rencontrés et y ont parlé de leurs travaux. Cet ouvrage est composé des articles associés aux différentes conférences qui s'y sont tenues.