Models of Massive Parallelism

Analysis of Cellular Automata and Neural Networks

Max Garzon (Autor)

Buch | Softcover

XIV, 272 Seiten

2012 | 1. Softcover reprint of the original 1st ed. 1995
Springer Berlin (Verlag)
978-3-642-77907-7 (ISBN)

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Locality is a fundamental restriction in nature. On the other hand, adaptive complex systems, life in particular, exhibit a sense of permanence and time lessness amidst relentless constant changes in surrounding environments that make the global properties of the physical world the most important problems in understanding their nature and structure. Thus, much of the differential and integral Calculus deals with the problem of passing from local information (as expressed, for example, by a differential equation, or the contour of a region) to global features of a system's behavior (an equation of growth, or an area). Fundamental laws in the exact sciences seek to express the observable global behavior of physical objects through equations about local interaction of their components, on the assumption that the continuum is the most accurate model of physical reality. Paradoxically, much of modern physics calls for a fundamen tal discrete component in our understanding of the physical world. Useful computational models must be eventually constructed in hardware, and as such can only be based on local interaction of simple processing elements.

1. Turing Computability and Complexity.- 1.1 Models of Sequential Computation.- 1.2 Complexity.- 1.3 Cellular Machines.- 1.4 Prerequisites.- References.- 2. Cellular Automata.- 2.1 Finite-State Automata.- 2.2 Regular Graphs.- 2.3 Local Rules and Global Maps.- 2.4 Fundamental Questions.- 2.5 Notation.- 2.6 Problems.- 2.7 Notes.- References.- 3. Linear Cellular Automata.- 3.1 Linear Rules.- 3.2 Basic Properties.- 3.3 Global Dynamics via Fractals.- 3.4 The Role of Linear Rules.- 3.5 Problems.- 3.6 Notes.- References.- 4. Semi-totalistic Automata.- 4.1 Semi-totalistic Rules.- 4.2 Construction and Computation Universality.- 4.3 Restricted Totalistic Rules.- 4.4 Threshold Automata.- 4.5 Problems.- 4.6 Notes.- References.- 5. Decision Problems.- 5.1 Algorithmic and Dynetic Problems.- 5.2 ID Euclidean Automata.- 5.3 2D Euclidean Automata.- 5.4 Noneuclidean Automata.- 5.5 Complexity Questions.- 5.6 Problems.- 5.7 Notes.- References.- 6. Neural and Random Boolean Networks.- 6.1 Types of Generalizations.- 6.2 Other Parallel Models.- 6.3 Summary of Results.- 6.4 Proofs.- 6.5 Problems.- 6.6 Notes.- References.- 7. General Properties.- 7.1 Metric Preliminaries.- 7.2 Basic Results.- 7.3 Injeetivity, Surjectivity and Local Reversibility.- 7.4 Some Generalizations.- 7.5 Problems.- 7.6 Notes.- References.- 8. Classification.- 8.1 Finite Networks.- 8.2 Wolfram Classification.- 8.3 Classification via Limit Sets.- 8.4 Mean Field Theory.- 8.5 Local Structure Theory.- 8.6 Other Classifications.- 8.7 Problems.- 8.8 Notes.- References.- 9. Asymptotic Behavior.- 9.1 Linear Rules.- 9.2 Exact Solution.- 9.3 Simulation in Continuous Systems.- 9.4 Observability.- 9.5 Problems.- 9.6 Notes.- References.- 10. Some Inverse Problems.- 10.1 Signals and Synchronization.- 10.2 Formal Language Recognition.-10.3 Picture Languages.- 10.4 Problems.- 10.5 Notes.- References.- 11. Real Computation.- 11.1 Representation and Primitives.- 11.2 Exact Computation.- 11.3 Approximate Computation by Neural Nets.- 11.4 Problems.- 11.5 Notes.- References.- 12. A Bibliography of Applications.- 12.1 Physics.- 12.2 Chemistry.- 12.3 Biology.- 12.4 Computer Science.- 12.5 Artificial Intelligence and Cognitive Science.- 12.6 Miscellaneous.- References.- Author Index.- Symbol Index.

Erscheint lt. Verlag	12.2.2012
Reihe/Serie	Texts in Theoretical Computer Science. An EATCS Series
Zusatzinfo	XIV, 272 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	445 g
Themenwelt	Informatik ► Software Entwicklung ► User Interfaces (HCI)
	Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
Schlagworte	Algorithmic Complexity • algorithmische Komplexität • algorithms • Automata • Cellular Automata • Complexity • Computational Complexity • (diskrete) neural networks • (diskrete) neuronale Netze • Dynamical Systems • Dynamische Systeme • kompakte Räume • Network • Neural networks • neutral networks • topology of compact spaces • zellulare Automaten
ISBN-10	3-642-77907-7 / 3642779077
ISBN-13	978-3-642-77907-7 / 9783642779077
Zustand	Neuware