Boolean Logic, Expressions and Theories


Book Description

The Boolean function network is a systematical approach proposed for the inference of gene regulatory networks and related Boolean functions. This procedure utilizes two steps to integrate the hidden Markov model, likelihood ratio test and Boolean functions for discovering direct pairwise relations between genes from time-course transcriptome data. In this compilation, the authors justify the need for this novel approach and describe the inference procedure. Next, an extended Boolean logic is introduced, denoted by LLT, called "star-finite" or "hyperfinite" logic. LLT is closely related to infinitary logics, which have been investigated extensively. Lastly, generalized Boolean functions are introduced, and an overview with regard to constructions of Golay complementary sequences from generalized Boolean functions is given.




Boolean Algebra and Its Applications


Book Description

Introductory treatment begins with set theory and fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. 1961 edition.




Boolean Functions


Book Description

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 Digital Systems


Book Description

A unique guide to using both modeling and simulation in digital systems design Digital systems design requires rigorous modeling and simulation analysis that eliminates design risks and potential harm to users. Introduction to Digital Systems: Modeling, Synthesis, and Simulation Using VHDL introduces the application of modeling and synthesis in the effective design of digital systems and explains applicable analytical and computational methods. Through step-by-step explanations and numerous examples, the author equips readers with the tools needed to model, synthesize, and simulate digital principles using Very High Speed Integrated Circuit Hardware Description Language (VHDL) programming. Extensively classroom-tested to ensure a fluid presentation, this book provides a comprehensive overview of the topic by integrating theoretical principles, discrete mathematical models, computer simulations, and basic methods of analysis. Topical coverage includes: Digital systems modeling and simulation Integrated logic Boolean algebra and logic Logic function optimization Number systems Combinational logic VHDL design concepts Sequential and synchronous sequential logic Each chapter begins with learning objectives that outline key concepts that follow, and all discussions conclude with problem sets that allow readers to test their comprehension of the presented material. Throughout the book, VHDL sample codes are used to illustrate circuit design, providing guidance not only on how to learn and master VHDL programming, but also how to model and simulate digital circuits. Introduction to Digital Systems is an excellent book for courses in modeling and simulation, operations research, engineering, and computer science at the upper-undergraduate and graduate levels. The book also serves as a valuable resource for researchers and practitioners in the fields of operations research, mathematical modeling, simulation, electrical engineering, and computer science.




Boolean Reasoning


Book Description

Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.




Set Theory


Book Description

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 important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the third edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It covers recent developments in the field and contains numerous exercises, along with updated and increased coverage of the background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory.




Duality Theories for Boolean Algebras with Operators


Book Description

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 operators. Givant addresses the two most recognized dualities (one algebraic and the other topological) and introduces a third duality, best understood as a hybrid of the first two. This text will be of interest to graduate students and researchers in the fields of mathematics, computer science, logic, and philosophy who are interested in exploring special or general classes of Boolean algebras with operators. Readers should be familiar with the basic arithmetic and theory of Boolean algebras, as well as the fundamentals of point-set topology.




Boole's Logic and Probability


Book Description

Since the publication of the first edition in 1976, there has been a notable increase of interest in the development of logic. This is evidenced by the several conferences on the history of logic, by a journal devoted to the subject, and by an accumulation of new results. This increased activity and the new results - the chief one being that Boole's work in probability is best viewed as a probability logic - were influential circumstances conducive to a new edition. Chapter 1, presenting Boole's ideas on a mathematical treatment of logic, from their emergence in his early 1847 work on through to his immediate successors, has been considerably enlarged. Chapter 2 includes additional discussion of the ``uninterpretable'' notion, both semantically and syntactically. Chapter 3 now includes a revival of Boole's abandoned propositional logic and, also, a discussion of his hitherto unnoticed brush with ancient formal logic. Chapter 5 has an improved explanation of why Boole's probability method works. Chapter 6, Applications and Probability Logic, is a new addition. Changes from the first edition have brought about a three-fold increase in the bibliography.