Journal article 1178 views 80 downloads
A coinductive approach to computing with compact sets
,
Dieter Spreen
Journal of Logic and Analysis, Volume: 8, Issue: 3, Pages: 1 - 35
Swansea University Author:
Ulrich Berger
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DOI (Published version): 10.4115/jla.2016.8.3
Abstract
Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first author it was shown how to extract certified algorithms worki...
| Published in: | Journal of Logic and Analysis |
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| ISSN: | 1759-9008 |
| Published: |
Journal of Logic and Analysis
2016
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa28975 |
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| Abstract: |
Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first author it was shown how to extract certified algorithms working with the signed digit representations from constructiveproofs. In this paper we lay the foundation for doing a similar thing with nonempty compact sets. It turns out that a representation by streams of finitely many digits is impossible and instead trees are needed. |
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| Keywords: |
program extraction, exact real number computation, computing with continuous objects, compact sets |
| Issue: |
3 |
| Start Page: |
1 |
| End Page: |
35 |