Boolean Functions

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This collection of papers presents a series of in-depth examinations of a variety of advanced topics related to Boolean functions and expressions. The chapters are written by some of the most prominent experts in their respective fields and cover topics ranging from algebra and propositional logic to learning theory, cryptography, computational complexity, electrical engineering, and reliability theory. Beyond the diversity of the questions raised and investigated in different chapters, a remarkable feature of the collection is the common thread created by the fundamental language, concepts, models, and tools provided by Boolean theory. Many readers will be surprised to discover the countless links between seemingly remote topics discussed in various chapters of the book. This text will help them draw on such connections to further their understanding of their own scientific discipline and to explore new avenues for research.

This introduction to Boolean algebra begins with an intuitive approach to set theory and an axiomatic account of the fundamentals of Boolean algebra, proceeding to concise accounts of applications to

This elementary treatment by a distinguished mathematician begins with the algebra of classes and proceeds to discussions of several different axiomatizations and Boolean algebra in the setting of the

This undergraduate-level describes the mathematics most needed in computer science. Bender and Williamson (both mathematics, U. of California, San Diego) cover Boolean functions and computer arithmeti

Mathematics for Electrical Engineering and Computing embraces many applications of modern mathematics, such as Boolean Algebra and Sets and Functions, and also teaches both discrete and continuous sys

By considering the size of the logical network needed to perform a given computational task, the intrinsic difficulty of that task can be examined. Boolean function complexity, the combinatorial study of such networks, is a subject that started back in the 1950s and has today become one of the most challenging and vigorous areas of theoretical computer science. The papers in this book stem from the London Mathematical Society Symposium on Boolean Function Complexity held at Durham University in July 1990. The range of topics covered will be of interest to the newcomer to the field as well as the expert, and overall the papers are representative of the research presented at the Symposium. Anyone with an interest in Boolean Function complexity will find that this book is a necessary purchase.

Communication Complexity describes a new intuitive model for studying circuit networks that captures the essence of circuit depth. Although the complexity of boolean functions has been studied for alm

This presentation on the basics of Boolean algebra has ranked among the fundamental books on this important subject in mathematics and computing science since its initial publication in 1963. Concise

This book represents a significant step towards bridging the areas of Boolean satisfiability and constraint satisfaction by providing theoretical explanations for why SAT-solvers are efficient on cert

This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a class of complexes and featuring matroids as central to the theory. The

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 descrip

This volume concentrates on the structure of Boolean algebras and rings as developed through simpler algebraic systems. The algebra of logic and set theory appears as applications or illustrations thr

This book is an informal, although systematic presentation of lectures given by the authors on Boolean algebras, intended for advanced undergraduates and beginning graduate students. In a bold and ref

The Boolean network (BN) is a mathematical model of genetic networks and other biological networks. Although extensive studies have been done on BNs from a viewpoint of complex systems, not so many st

In this new text, Steven Givant—the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski—develops three theories of duality for Boolean algebras with opera

This book brings to bear a body of logic synthesis techniques, in order to contribute to the analysis and control of Boolean Networks (BN) for modeling genetic diseases such as cancer. The authors pro

This book provides an overview of automatic test pattern generation (ATPG) and introduces novel techniques to complement classical ATPG, based on Boolean Satisfiability (SAT). A fast and highly fault

This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory. It provides an exposition of some of the most import

In Test Pattern Generation using Boolean Proof Engines, we give an introduction to ATPG. The basic concept and classical ATPG algorithms are reviewed. Then, the formulation as a SAT problem is conside

Written for students and researchers in the fields of behavioral sciences, history and logic, this textbook on comparative methods with Boolean algebra explains how these mathematical theories are use

An investigation of the logical flexibility principles needed for a formal semantic account of coordination, plurality, and scope in natural language. Since the early work of Montague, Boolean seman

Mathematician Harald Bohr, motivated by questions about which functions could be represented by a Dirichlet series, devised the theory of almost periodic functions during the 1920s. His groundbreaking

For courses in college algebra. Ties concepts together using a functions approach The Concepts Through Functions Series introduces functions at the start of each text, and maintains a continuo

Property testing is concerned with the design of super-fast algorithms for the structural analysis of large quantities of data. The aim is to unveil global features of the data, such as determining whether the data has a particular property or estimating global parameters. Remarkably, it is possible for decisions to be made by accessing only a small portion of the data. Property testing focuses on properties and parameters that go beyond simple statistics. This book provides an extensive and authoritative introduction to property testing. It provides a wide range of algorithmic techniques for the design and analysis of tests for algebraic properties, properties of Boolean functions, graph properties, and properties of distributions.

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use--from our computers and cars, to our kitchen gadgets and home appliances. How did a system

This book covers novel research on construction and analysis of optimal cryptographic functions such as almost perfect nonlinear (APN), almost bent (AB), planar and bent functions. These functions hav

Pseudolinear Functions and Optimization is the first book to focus exclusively on pseudolinear functions, a class of generalized convex functions. It discusses the properties, characterizations, and a

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use--from our computers and cars, to our kitchen gadgets and home appliances. How did a system

Many mathematicians may never have heard of Bernstein functions, because in probability they are known as Laplace exponents, in harmonic analysis as negative definite functions, in complex analysis as

Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. T

This book gives an introduction to theories of computability from a mathematically sophisticated point of view. It treats not only 'the' theory of computability (created by Alan Turing and others in the 1930s), but also a variety of other theories (of Boolean functions, automata and formal languages). These are addressed from the classical perspective of their generation by grammars and from the modern perspective as rational cones. The treatment of the classical theory of computable functions and relations takes the form of a tour through basic recursive function theory, starting with an axiomatic foundation and developing the essential methods in order to survey the most memorable results of the field. This authoritative account by one of the leading lights of the subject will prove exceptionally useful reading for graduate students, and researchers in theoretical computer science and mathematics.

Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. T

The famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions) are analyzed through several zeta functions built over those zeros. These ‘seco

The theory of generalized hypergeometric functions is fundamental in the field of mathematical physics, since all the commonly used functions of analysis (Besse] Functions, Legendre Functions, etc.) are special cases of the general functions. The unified theory provides a means for the analysis of the simpler functions and can be used to solve the more complicated equations in physics. The generalized Gauss function is also used in mathematical statistics and the basic analogues of the Gauss functions have applications in the field of number theory. Dr Slater's treatment leads on from a discussion of the Gauss functions to the basic hypergeometric functions, the hypergeometric integrals, bilateral series and Appel series. This book was planned jointly with the late Professor W. N. Bailey as an extended revision of his Cambridge Mathematical Tract (1935) on the subject and Dr Slater has continued it single-handed since Professor Bailey's death, incorporating in it the results of many of

Chapter 1 introduces elementary classical special functions. Gamma, beta, psi, zeta functions, hypergeometric functions and the associated special functions, generalizations to Meijer's G and Fox's H

In its first six chapters this 2006 text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?' Accordingly, it is based on the idea of inverting integrals which arise in the theory of differential equations and, in particular, the differential equation that describes the motion of a simple pendulum. The later chapters present a more conventional approach to the Weierstrass functions and to elliptic integrals, and then the reader is introduced to the richly varied applications of the elliptic and related functions. Applications spanning arithmetic (solution of the general quintic, the functional equation of the Riemann zeta function), dynamics (orbits, Euler's equations, Green's functions), and also probability and statistics, are discussed.

In its first six chapters this 2006 text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?' Accordingly, it is based on the idea of inverting integrals which arise in the theory of differential equations and, in particular, the differential equation that describes the motion of a simple pendulum. The later chapters present a more conventional approach to the Weierstrass functions and to elliptic integrals, and then the reader is introduced to the richly varied applications of the elliptic and related functions. Applications spanning arithmetic (solution of the general quintic, the functional equation of the Riemann zeta function), dynamics (orbits, Euler's equations, Green's functions), and also probability and statistics, are discussed.

This volume presents students with problems and exercises designed to illuminate the properties of functions and graphs. The 1st part of the book employs simple functions to analyze the fundamental m

Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included. Other topics include q-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and applica