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Journal article 1605 views 283 downloads

Computability of Operators on Continuous and Discrete Time Streams

John Tucker Orcid Logo, Jeffrey I Zucker

Computability, Volume: 3, Issue: 1, Pages: 9 - 44

Swansea University Author: John Tucker Orcid Logo

DOI (Published version): 10.3233/COM-14024

Abstract

A stream is a sequence of data indexed by time. The behaviour of natural and artificial systems can be modelled bystreams and stream transformations. There are two distinct types of data stream: streams based on continuous time and streamsbased on discrete time. Having investigated case studies of b...

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Published in: Computability
Published: 2014
Online Access: http://content.iospress.com/articles/computability/com024
URI: https://cronfa.swan.ac.uk/Record/cronfa21548
first_indexed 2015-05-20T02:03:26Z
last_indexed 2019-07-17T20:18:32Z
id cronfa21548
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spelling 2019-07-17T15:41:47.3707829 v2 21548 2015-05-19 Computability of Operators on Continuous and Discrete Time Streams 431b3060563ed44cc68c7056ece2f85e 0000-0003-4689-8760 John Tucker John Tucker true false 2015-05-19 MACS A stream is a sequence of data indexed by time. The behaviour of natural and artificial systems can be modelled bystreams and stream transformations. There are two distinct types of data stream: streams based on continuous time and streamsbased on discrete time. Having investigated case studies of both kinds separately, we have begun to combine their study in aunified theory of stream transformers, specified by equations. Using only the standard mathematical techniques of topology, wehave proved continuity properties of stream transformers. Here, in this sequel, we analyse their computability. We use the theoryof computable functions on algebras to design two distinct methods for defining computability on continuous and discrete timestreams of data from a complete metric space. One is based on low-level concrete representations, specifically enumerations, andthe other is based on high-level programming, specifically ‘while’ programs, over abstract data types. We analyse when thesemethods are equivalent. We demonstrate the use of the methods by showing the computability of an analog computing system.We discuss the idea that continuity and computability are important for models of physical systems to be “well-posed”. Journal Article Computability 3 1 9 44 analog computing, computing on streams, many-sorted algebras, topological algebras, stream operators, synchronous concurrent algorithms 31 12 2014 2014-12-31 10.3233/COM-14024 http://content.iospress.com/articles/computability/com024 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2019-07-17T15:41:47.3707829 2015-05-19T14:11:48.7988323 John Tucker 0000-0003-4689-8760 1 Jeffrey I Zucker 2 0021548-07062016115028.pdf Tucker-Zucker-Computability_and_streams.pdf 2016-06-07T11:50:28.2430000 Output 434171 application/pdf Accepted Manuscript true 2016-06-07T00:00:00.0000000 true
title Computability of Operators on Continuous and Discrete Time Streams
spellingShingle Computability of Operators on Continuous and Discrete Time Streams
John Tucker
title_short Computability of Operators on Continuous and Discrete Time Streams
title_full Computability of Operators on Continuous and Discrete Time Streams
title_fullStr Computability of Operators on Continuous and Discrete Time Streams
title_full_unstemmed Computability of Operators on Continuous and Discrete Time Streams
title_sort Computability of Operators on Continuous and Discrete Time Streams
author_id_str_mv 431b3060563ed44cc68c7056ece2f85e
author_id_fullname_str_mv 431b3060563ed44cc68c7056ece2f85e_***_John Tucker
author John Tucker
author2 John Tucker
Jeffrey I Zucker
format Journal article
container_title Computability
container_volume 3
container_issue 1
container_start_page 9
publishDate 2014
institution Swansea University
doi_str_mv 10.3233/COM-14024
url http://content.iospress.com/articles/computability/com024
document_store_str 1
active_str 0
description A stream is a sequence of data indexed by time. The behaviour of natural and artificial systems can be modelled bystreams and stream transformations. There are two distinct types of data stream: streams based on continuous time and streamsbased on discrete time. Having investigated case studies of both kinds separately, we have begun to combine their study in aunified theory of stream transformers, specified by equations. Using only the standard mathematical techniques of topology, wehave proved continuity properties of stream transformers. Here, in this sequel, we analyse their computability. We use the theoryof computable functions on algebras to design two distinct methods for defining computability on continuous and discrete timestreams of data from a complete metric space. One is based on low-level concrete representations, specifically enumerations, andthe other is based on high-level programming, specifically ‘while’ programs, over abstract data types. We analyse when thesemethods are equivalent. We demonstrate the use of the methods by showing the computability of an analog computing system.We discuss the idea that continuity and computability are important for models of physical systems to be “well-posed”.
published_date 2014-12-31T11:44:39Z
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score 11.088971

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