Boolean Systems: Topics in Asynchronicity - Softcover

Vlad, Serban E.

Softcover

ISBN 10: 0323954227 ISBN 13: 9780323954228

Publisher: Academic Press, 2023

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.

• Presents a consistent and original theory of the discrete-time Boolean asynchronous systems, which are useful for mathematicians and computer scientists interested in Boolean Networks, dynamical systems, and modeling.
• Studies the flows and equations of evolution, nullclines, dependence on initial conditions, periodicity, path-connectedness, topological transitivity, chaos, nonwandering points, invariance, connectedness, and separation, as well as the basins of attraction, attractors, stability, and time-reversal symmetry.
• Explains the fundamental operating mode of the input systems and the combinational systems (systems without feedback).
• Includes a chapter of applications of the Boolean systems and their modeling techniques.
• Makes use of the unbounded delay model of computation of the Boolean functions.

About this title

About the Author

Serban E. Vlad is an analyst programmer at the Oradea City Hall, Romania. He is a member of the Society of Mathematical Sciences from Romania SSMR and of the Association of Applied Mathematics and Mechanics from Germany GAMM. He is the author of many papers and several books and book chapters.

From the Back Cover

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.

Edition details

• Publisher: Academic Press
• Publication date: 2023
• Language: English
• ISBN 10: 0323954227
• ISBN 13: 9780323954228
• Binding: Paperback
• Edition number: 1
• Number of pages: 456