Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks

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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 timeĀ­ 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 fundamenĀ­ 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.

Author(s): Max Garzon
Series: Texts in Theoretical Computer Science. An EATCS Series
Publisher: Springer
Year: 1995

Language: English
Pages: 272
Tags: Computation by Abstract Devices;Artificial Intelligence (incl. Robotics);Statistical Physics, Dynamical Systems and Complexity

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