Synopses & Reviews
This is a textbook and a reference book on Boolean functions, i.e. functions of binary vectors assuming at most two values 0 and 1. First, the conventional theory and its applications in computer engineering are covered. Then - revisiting and deepening the historical notation of George Boole - Boolean operators, typically NOT, AND, and OR are replaced by standard addition, subtraction,and multiplication. This is shown to be extremely useful in the stochastic theory of Boolean functions. The latter is covered at considerable depth with numerous applications mostly in the field of reliability systems theory (fault-trees etc.). In the context of fault tree evaluation several modern Boolean algorithms are discussed, and aspects of PASCAL implementations are reviewed. The book as a whole should help theoretically minded practitioners to a clearer and deeper understanding of Boolean functions and it should give numerous hints for practical numerical work via typically Boolean computer programs.
Synopsis
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 easy to use information, and standard books, such as, on switching circuits theory and reliability theory, are mostly somewhat narrow as far as Boolean analysis is concerned. Further- more, in books on switching circuits theory the relevant stochastic theory is not covered. Aspects of the probabilistic theory of Boolean functions are treated in some works on reliability theory, but the results deserve a much broader interpre- tation. Just as the applied theory (e. g. of the Laplace transform) is useful in control theory, renewal theory, queueing theory, etc., the applied theory of Boolean functions (of indicator variables) can be useful in reliability theory, switching circuits theory, digital diagnostics and communications theory. This book is aimed at providing a sufficiently deep understanding of useful results both in practical work and in applied research. Boolean variables are restricted here to indicator or O/l variables, i. e. variables whose values, namely 0 and 1, are not free for a wide range of interpretations, e. g. in digital electronics 0 for L ==low voltage and 1 for H == high voltage.
Table of Contents
Contents: Notation and Glossary of Fundamental Terms and Symbols.- Fundamental Concepts.- Diagrams for Boolean Analysis.- Representations (Forms) and Types of Boolean Functions.- Minimal Disjunctive Normal Forms.- Boolean Difference Calculus.- Boolean Functions Without Boolean Operators.- Stochastic Theory of Boolean Functions.- Stochastic Theory of Boolean Indicator Processes.- Some Algorithms and Computer Programs for Boolean Analysis.- Appendix: Probability Theory Refresher.- Solutions of the Exercises for §§ 2 through 11.- References.- Subject Index.