Boolean Systems

Boolean Systems: Topics in Asynchroniticy presents a consistent and original mathematical theory of the Boolean asynchronous systems. The purpose of the book is to set forth the concepts of such a theory, resulting from synchronous Boolean systems theory and mostly from the real systems theory, by analogy, and to indicate the way that known synchronous deterministic concepts generate new asynchronous nondeterministic concepts. The Boolean functions may be iterated either asynchronously, when their coordinates are computed independently of each other, or synchronously, when their coordinates are computed at the same time. Author Serban E. Vlad presents the first possibility in this book, which is addressed to mathematicians and computer scientists who are interested in Boolean systems and their use in modelling. The reader will be introduced to the dependence on the initial conditions, periodicity, path-connectedness, topological transitivity, and chaos. A property of major importance is invariance, which is present in five versions. In relation with it, the reader will study the maximal invariant subset, the minimal invariant superset, the minimal invariant subset, connectedness, separation, as well as the basins of attraction and the attractors. The stability of the systems and their time reversal symmetry end the topics that refer to the systems without input. The rest of the book is concerned with the input systems. The most consistent chapters refer to the fundamental operating mode, and to the combinational systems (systems without feedback). The last chapter, called wires, gates and flip-flops, presents a variety of applications. Presents a consistent and original theory of the Boolean asynchronous systems, which are useful for mathematicians and computer scientists who are interested in modelling dynamic systems and flow Conveys the role of discrete time morphisms of Boolean functions, including signals, computation functions, flows and equations of evolution, nullclines, dependence on initial conditions, periodicity, definitions of the pathdependent set, topological transitivity, chaos, nonwandering points, definitions of invariant sets, connectedness and separation, as well as basins of attraction, attractors, and stability Explains how to develop and apply a variety of computational modelling techniques derived from time-reversal symmetry, generator functions with one parameter, input flows and equations of evolution, input systems, the fundamental operating mode, combinatorial systems, wires, gates, and flip-flops Includes a chapter covering a variety of applications of Boolean systems and their modelling techniques