Boolean Functions : With Engineering Applications and Computer Programs

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.