Models of Massive Parallelism

This textbook presents analytic methods and results for exploring and understanding cellular automata and discrete neural networks. The book includes exercises and bibliographies and may serve also as a reference manual.

Klappentext

This textbook provides an introduction to the fundamental models of massively parallel computation, the most important technique for high-performance computing. It presents a coherent exposition of analytic methods and results for the exploration and understanding of cellular automata and discrete neural networks as computational and dynamical systems. The book will be useful also as a reference manual to the scattered literature in the field. Each chapter includes a separate bibliography, as well as pointers to historically relevant papers, and gives exercise problems for the reader.

Inhalt

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.