Boolean Functions With Engineering Applications and Computer Programs

Boolean Functions With Engineering Applications and Computer Programs / by Winfried G. Schneeweiss.

Modern systems engineering (e. g. switching circuits design) and operations research (e. g. reliability systems theory) use Boolean functions with increasing regularity. For practitioners and students in these fields books written for mathe­ maticians are in several respects not the best source of e...

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Bibliographic Details
Main Author: Schneeweiss, Winfried G. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1989.
Edition:1st ed. 1989.
Series:Springer eBook Collection.
Subjects:
Electrical engineering.
Applied mathematics.
Engineering mathematics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1 Notation and Glossary of Fundamental Terms and Symbols
  • 2 Fundamental Concepts
  • 2.1 Boolean Indicator Variables and All Their Functions of One and Two Variables
  • 2.2 Axioms and Elementary Laws of Boolean Algebra
  • 2.3 Polynomials, Vectors, and Matrices with Boolean Elements
  • Exercises
  • 3 Diagrams for Boolean Analysis
  • 3.1 Standard Graphical Representation of Boolean Functions
  • 3.2 Binary Decision Diagrams
  • 3.3 Karnaugh Maps
  • 3.4 Switching Network Graphs (Logic Diagrams) and Syntax Diagrams
  • 3.5 Venn Diagrams
  • 3.6 State Transition Graphs
  • 3.7 Communications Graphs
  • 3.8 Reliability Block Diagrams
  • 3.9 Flowcharts
  • 3.10 Petri Nets
  • Exercises
  • 4 Representations (Forms) and Types of Boolean Functions
  • 4.1 Negation (Complement)
  • 4.2 Special Terms
  • 4.3 Normal Forms and Canonical Normal Forms
  • 4.4 Disjunctive Normal Forms of Disjoint Terms
  • 4.5 Boolean Functions with Special Properties
  • 4.6 Recursive Definition of Boolean Functions
  • 4.7 Hazards
  • Exercises
  • 5 Minimal Disjunctive Normal Forms
  • 5.1 General Considerations
  • 5.2 Finding All Prime Implicants of a Boolean Function
  • 5.3 Minimization
  • Exercises
  • 6 Boolean Difference Calculus
  • 6.1 Exclusiv-Disjunction Form Without Negated Variables
  • 6.2 Concepts of Boolean Differences
  • 6.3 Basic Rules of Boolean Difference Calculus
  • 6.4 Diagnosing Permanent Faults in Switching Networks
  • Exercises
  • 7 Boolean Functions Without Boolean Operators
  • 7.1 Fundamental Concepts and Consequences
  • 7.2 Transformation of Boolean Functions of Indicator Variables to Multilinear Form
  • 7.3 Coherence Revisited
  • Exercises
  • 8 Stochastic Theory of Boolean Functions
  • 8.1 Probability of a Binary State
  • 8.2 Probability of the Value 1 of a Boolean Function
  • 8.3 Approximate Probability of the Value 1
  • 8.4 Moments of Boolean Functions
  • Exercises
  • 9 Stochastic Theory of Boolean Indicator Processes
  • 9.1 Mean Duration of States in the Markov Model
  • 9.2 Mean Duration of Boolean Functions’ Values
  • 9.3 Mean Frequency of Changes of Functions’ Values
  • 9.4 The Distribution of Residual Life Times
  • Exercises
  • 10 Some Algorithms and Computer Programs for Boolean Analysis
  • 10.1 Computing Values of a Boolean Function
  • 10.2 Canonical Representations of a Boolean Function
  • 10.3 Probability of a Given Value of a Boolean Function
  • 10.4 Algorithms for Making the Terms of a Given DNF Disjoint
  • 10.5 Selected Set Manipulations
  • Exercises
  • 11 Appendix: Probability Theory Refresher
  • 11.1 Boolean Algebra of Sets
  • 11.2 Elementary Probability Calculus
  • 11.3 Random Variables and Random Processes
  • 11.4 Elementary Renewal Theory
  • 11.5 Laplace Transform Refresher
  • Exercises
  • Solutions of the exercises for §§ 2 through 11
  • References.

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