Boolean Functions

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.