The Kolmogorov metric and a classification of linear cellular automata.
Item
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Title
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The Kolmogorov metric and a classification of linear cellular automata.
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Identifier
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AAI9405515
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identifier
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9405515
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Creator
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D'Alotto, Louis A.
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Contributor
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Adviser: Charles Giardina
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Date
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1993
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Language
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English
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Publisher
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City University of New York.
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Subject
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Computer Science
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Abstract
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The idea of classifying linear cellular automata by their dynamical behavior was initiated by Stephen Wolfram. Robert Gilman later brought this idea into a mathematical perspective when he introduced a probabilistic/topological classification of linear automata. This dissertation generalizes the classification results of Gilman by utilizing a more general, and more applicable, non-archimedean metric that was originally devised by Kolmogorov. The classification utilizes methods and results from point set topology, product measure theory and ergodic theory. Linear automata are then divided into three classes whereby the automata in each class seem to correspond to different dynamical behavior. These classification results are then applied to the convolution operation of signal processing to classify the functions of this operation for signals taking values in Z{dollar}\sb2.{dollar}.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
