Boolean Systems - by Serban E Vlad (Paperback)

Book Synopsis

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. In Boolean Systems: Topics in Asynchronicity, a book addressed to mathematicians and computer scientists interested in Boolean systems and their use in modelling, author Serban E. Vlad presents a consistent and original mathematical theory of the discrete-time Boolean asynchronous systems. The purpose of the book is to set forth the concepts of such a theory, resulting from the synchronous Boolean system theory and mostly from the synchronous real system theory, by analogy, and to indicate the way in which known synchronous deterministic concepts generate new asynchronous nondeterministic concepts. 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 to it, the reader will study the maximal invariant subsets, the minimal invariant supersets, the minimal invariant subsets, connectedness, separation, the basins of attraction, and 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 input systems. The most consistent chapters of this part of the book refer to the fundamental operating mode and to the combinational systems (systems without feedback). The chapter Wires, Gates, and Flip-Flops presents a variety of applications. The first appendix addresses the issue of continuous time, and the second one sketches the important theory of Daizhan Cheng, which is put in relation to asynchronicity. The third appendix is a bridge between asynchronicity and the symbolic dynamics of Douglas Lind and Brian Marcus.

Review Quotes

"The book under consideration consists of 37 Chapters and 3 Appendices. In it mathematical theory of the Boolean asynchronous systems is presented. The first chapters are introductory about the system and its dependence on the initial conditions, periodicity, path-connectedness, topological transitivity and chaos. For the Boolean systems one very important property is the invariance. For this reason the author presents the study of the maximal invariant subset, the minimal invariant superset, the minimal invariant subset, connectedness, separation, basin of attractions and attractors. The stability of the autonomous systems is studied together with their time-reversal symmetry. Then the systems with input are presented with the generator functions.... The book is rich of examples, which makes it interesting not only for mathematicians but also for computer scientists." --Angela Slavova, zbMATHOpen