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Domains for Computation in Mathematics, Physics and Exact Real Arithmetic

Published online by Cambridge University Press:  15 January 2014

Abbas Edalat
Abbas Edalat*
Affiliation:
Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen's Gate London SW7 2BZ, UK.E-mail: [email protected]
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Abstract

We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions. It is shown how these models have a logical and effective presentation and how they are used to give a computational framework in several areas in mathematics and physics. These include fractal geometry, where new results on existence and uniqueness of attractors and invariant distributions have been obtained, measure and integration theory, where a generalization of the Riemann theory of integration has been developed, and real arithmetic, where a feasible setting for exact computer arithmetic has been formulated. We give a number of algorithms for computation in the theory of iterated function systems with applications in statistical physics and in period doubling route to chaos; we also show how efficient algorithms have been obtained for computing elementary functions in exact real arithmetic.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 3 , Issue 4 , December 1997 , pp. 401 - 452
Copyright
Copyright © Association for Symbolic Logic 1997

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