Boolean Systems: Topics in Asynchronicity

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.