Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks (Texts in Theoretical Computer Science. An EATCS Series)

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. 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. Front Matter....Pages I-XIV Turing Computability and Complexity....Pages 1-15 Cellular Automata....Pages 17-38 Linear Cellular Automata....Pages 39-62 Semi-totalistic Automata....Pages 63-78 Decision Problems....Pages 79-96 Neural and Random Boolean Networks....Pages 97-116 General Properties....Pages 117-139 Classification....Pages 141-166 Asymptotic Behavior....Pages 167-198 Some Inverse Problems....Pages 199-229 Real Computation....Pages 231-254 A Bibliography of Applications....Pages 255-262 Back Matter....Pages 263-274