Boolean Systems: Topics in Asynchronicity

Boolean functions can be iterated either asynchronously or synchronously, with the latter resulting in new asynchronous nondeterministic concepts. This book provides a mathematical theory of discrete-time Boolean asynchronous systems, covering initial conditions, periodicity, path-connectedness, topological transitivity, chaos, invariance, maximal invariant subsets, minimal invariant supersets, minimal invariant subsets, connectedness, separation, basins of attraction, and attractors. The stability of systems and their time-reversal symmetry are discussed, and input systems are explored, with a focus on the fundamental operating mode and combinational systems.

Format: Paperback / softback
Length: 456 pages
Publication date: 01 January 2023
Publisher: Elsevier Science & Technology

The Boolean functions can be iterated either asynchronously, where their coordinates are computed independently of each other, or synchronously, where their coordinates are computed simultaneously. In Boolean Systems: Topics in Asynchronicity, a book aimed at mathematicians and computer scientists interested in Boolean systems and their applications in modelling, author Serban E. Vlad presents a comprehensive and original mathematical theory of discrete-time Boolean asynchronous systems. The primary objective of the book is to establish the concepts of such a theory, drawing inspiration from synchronous Boolean system theory and, to a significant extent, synchronous real system theory through analogy. The book aims to demonstrate how known synchronous deterministic concepts can lead to the generation of new asynchronous nondeterministic concepts. The reader will be introduced to various important concepts, including dependence on initial conditions, periodicity, path-connectedness, topological transitivity, and chaos. Invariance, a property of paramount significance, is explored in five different versions. The reader will delve into topics such as maximal invariant subsets, minimal invariant supersets, minimal invariant subsets, connectedness, separation, basins of attraction, and attractors. The stability of the systems and their time-reversal symmetry conclude the discussions related to systems without input. The remaining chapters of the book focus on input systems. The most coherent chapters in this part of the book revolve around the fundamental operating mode and combinational systems (systems without feedback). The chapter titled "Wires, Gates, and Flip-Flops" showcases a wide range of applications. The first appendix addresses the issue of continuous time, while the second appendix provides a sketch of the important theory of Daizhan Cheng, which is related to asynchronicity.

Weight: 450g
Dimension: 235 x 191 (mm)
ISBN-13: 9780323954228