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A coinductive approach to computing with compact sets

Ulrich Berger Orcid Logo, Dieter Spreen

Journal of Logic and Analysis, Volume: 8, Issue: 3, Pages: 1 - 35

Swansea University Author: Ulrich Berger Orcid Logo

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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...

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Published in: Journal of Logic and Analysis
ISSN: 1759-9008
Published: Journal of Logic and Analysis 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa28975
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first_indexed 2016-06-21T18:24:35Z
last_indexed 2020-08-03T12:45:25Z
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spelling 2020-08-03T12:45:03.2196095 v2 28975 2016-06-21 A coinductive approach to computing with compact sets 61199ae25042a5e629c5398c4a40a4f5 0000-0002-7677-3582 Ulrich Berger Ulrich Berger true false 2016-06-21 SCS 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. Journal Article Journal of Logic and Analysis 8 3 1 35 Journal of Logic and Analysis 1759-9008 program extraction, exact real number computation, computing with continuous objects, compact sets 31 12 2016 2016-12-31 10.4115/jla.2016.8.3 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2020-08-03T12:45:03.2196095 2016-06-21T15:41:38.1544332 Ulrich Berger 0000-0002-7677-3582 1 Dieter Spreen 2 28975__17829__6b054da02cbc4f2db8fed1b13eea736d.pdf 28975.pdf 2020-08-03T12:43:18.9913562 Output 394514 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution 3.0 License (CC-BY). true eng http://creativecommons.org/licenses/by/3.0/
title A coinductive approach to computing with compact sets
spellingShingle A coinductive approach to computing with compact sets
Ulrich Berger
title_short A coinductive approach to computing with compact sets
title_full A coinductive approach to computing with compact sets
title_fullStr A coinductive approach to computing with compact sets
title_full_unstemmed A coinductive approach to computing with compact sets
title_sort A coinductive approach to computing with compact sets
author_id_str_mv 61199ae25042a5e629c5398c4a40a4f5
author_id_fullname_str_mv 61199ae25042a5e629c5398c4a40a4f5_***_Ulrich Berger
author Ulrich Berger
author2 Ulrich Berger
Dieter Spreen
format Journal article
container_title Journal of Logic and Analysis
container_volume 8
container_issue 3
container_start_page 1
publishDate 2016
institution Swansea University
issn 1759-9008
doi_str_mv 10.4115/jla.2016.8.3
publisher Journal of Logic and Analysis
document_store_str 1
active_str 0
description 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.
published_date 2016-12-31T03:35:20Z
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score 11.013619

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