Binary Periodic Signals and Flows


Serban E. Vlad
The Romanian Society of Applied and Industrial Mathematics, Oradea, Romania

Series: Mathematics Research Developments
BISAC: MAT003000

The signals from digital electrical engineering are modeled by discrete time and real time functions, whose values are binary n-tuples and which are also called signals. The asynchronous circuits, representing the devices that work with such signals, are modeled by Boolean autonomous deterministic regular asynchronous systems, shortly by asynchronous flows. The attribute ‘Boolean’ vaguely refers to the binary Boole algebra; ‘autonomous’ means that there is no input; ‘deterministic’ means the existence of a unique state function; and ‘regular’ indicates the existence of a Boolean function that iterates its coordinates independently on each other (i.e. asynchronously). Strong analogies exist with the real, usual dynamical systems.

The purpose of this research monograph is to study the periodicity of the signals and of their values, as well as the periodicity of the asynchronous flows. The monograph addresses systems theory and computer science that apply to researchers, but it is also interesting to those that study periodicity itself. From this last perspective, the signals may be thought of as functions with finitely many values. At the same time, the asynchronous flows may be considered as special cases of variable structure systems.

The bibliography consists of works of real, dynamical systems that produce analogies. (Imprint: Nova)



Table of Contents


Chapter 1. Preliminaries

Chapter 2. The Main Definitions on Periodicity

Chapter 3. Eventually Constant Signals

Chapter 4. Constant Signals

Chapter 5. Eventually Periodic Points

Chapter 6. Eventually Periodic Signals

Chapter 7. Periodic Points

Chapter 8. Periodic Signals

Chapter 9. Examples

Chapter 10. Computation Functions

Chapter 11. Flows

Chapter 12. A Wider Point of View: Control and Systems

Chapter 13. Eventually Constant Flows

Chapter 14. Constant Flows

Chapter 15. The Periodicity of the Flows


Appendix A. Notations

Appendix B. Index

Appendix C. Lemmas


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The monograph addresses systems theory and computer science that apply to researchers, but it is also interesting to those that study periodicity itself.

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