Boolean Systems: Topics in Asynchroniticy presents a consistent and original mathematical theory of Boolean asynchronous systems. The book sets forth the concepts of the theory that is a result of synchronous Boolean systems theory, but mostly from real systems theory, by analogy, to indicate the way that known synchronous deterministic concepts generate new asynchronous nondeterministic concepts. Readers will be introduced to dependence on initial conditions, periodicity, path-connectedness, topological transitivity, and chaos. Other sections cover input systems, with content spanning fundamental operating mode, combinational systems (systems without feedback), wires, gates, flip-flops, and applications. 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 modeling. Conveys the role of discrete time morphisms of Boolean functions, including signals, computation functions, flows and equations of evolution, nullclines, dependence on initial conditions, periodicity, definitions of the path dependent set, topological transitivity, chaos, nonwandering points, definitions of invariant sets, connectedness and separation, as well as basins of attraction, attractors and stability Explains how to develop and apply a variety of computational modeling techniques derived from time-reversal symmetry, generator functions with one parameter, input flows and equations of evolution, input systems, the fundamental operating mode, combinatorial systems, wires, gates and flip-flops Includes a chapter covering a variety of applications of Boolean systems and their modeling techniques INDICE: 1. Boolean Functions2. Morphisms of Generator Functions3. State Portraits 4. Signals 5. Computation Functions and Progressiveness 6. Flows and Equations of Evolution 7. Systems 8. Morphisms of Flows 9. Nullclines 10. Fixed points 11. Sources, Isolated Fixed Points, Transient Points, Sinks 12. Sets of Reachable States 13. Dependence on the Initial Conditions 14. Periodicity 15. Path Connectedness and Topological Transitivity 16. Chaos 17. Nonwandering Points and Poisson Stability 18. Invariance 19. Relatively Isolated Sets, Isolated Set 20. Maximal Invariant Subset 21. Minimal Invariant Superset 22. Minimal Invariant Subset 23. Connectedness and Separation 24. Basins of Attraction 25. The Basins of Attraction of the States 26. Local Basins of Attraction 27. Local Basins of Attraction of the States 28. Attractors 29. Stability 30. Time Reversal Symmetry 31. Generator functions with one parameter 32. Input Flows and Equations of Evolution 33. Input systems 34. The Fundamental (Operating) Mode 35. Combinational Systems with One Level 36. Combinational systems 37. Wires, Gates, and Flip FlopsAppendixA. Continuous Time B. Theory of ChengC. Notations
- ISBN: 978-0-323-95422-8
- Editorial: Academic Press
- Encuadernacion: Rústica
- Páginas: 380
- Fecha Publicación: 01/01/2023
- Nº Volúmenes: 1
- Idioma: Inglés