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Generalizing Computability Theory to Abstract Algebras

J. V. Tucker, J. I. Zucker, John Tucker Orcid Logo

Turing’s Revolution, Pages: 127 - 160

Swansea University Author: John Tucker Orcid Logo

DOI (Published version): 10.1007/978-3-319-22156-4_5

Abstract

We present a survey of our work over the last four decades on generalizations of computability theory to many-sorted algebras. The following topics are discussed, among others: (1) abstract v concrete models of computation for such algebras; (2) computability and continuity, and the use of many-sort...

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Published in: Turing’s Revolution
ISBN: 978-3-319-22156-4
Published: Basel Bikhauser/Springer 2016
Online Access: http://link.springer.com/chapter/10.1007/978-3-319-22156-4_5
URI: https://cronfa.swan.ac.uk/Record/cronfa30876
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last_indexed 2018-09-06T18:33:22Z
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spelling 2018-09-06T12:53:21.5866546 v2 30876 2016-10-31 Generalizing Computability Theory to Abstract Algebras 431b3060563ed44cc68c7056ece2f85e 0000-0003-4689-8760 John Tucker John Tucker true false 2016-10-31 SCS We present a survey of our work over the last four decades on generalizations of computability theory to many-sorted algebras. The following topics are discussed, among others: (1) abstract v concrete models of computation for such algebras; (2) computability and continuity, and the use of many-sorted topological partial algebras, containing the reals; (3) comparisons between various equivalent and distinct models of computability; and(4) generalized Church-Turing theses. Book chapter Turing’s Revolution 127 160 Bikhauser/Springer Basel 978-3-319-22156-4 Computability and continuity, Computability on abstract structures, Computability on the reals, Generalized church-turing thesis, Generalized computability 21 1 2016 2016-01-21 10.1007/978-3-319-22156-4_5 http://link.springer.com/chapter/10.1007/978-3-319-22156-4_5 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2018-09-06T12:53:21.5866546 2016-10-31T10:06:53.1882903 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science J. V. Tucker 1 J. I. Zucker 2 John Tucker 0000-0003-4689-8760 3 0030876-31102016101607.pdf GeneralizingComputabilityTheoryToAbstractAlgebras.pdf 2016-10-31T10:16:07.7600000 Output 313850 application/pdf Accepted Manuscript true 2016-10-31T00:00:00.0000000 true
title Generalizing Computability Theory to Abstract Algebras
spellingShingle Generalizing Computability Theory to Abstract Algebras
John Tucker
title_short Generalizing Computability Theory to Abstract Algebras
title_full Generalizing Computability Theory to Abstract Algebras
title_fullStr Generalizing Computability Theory to Abstract Algebras
title_full_unstemmed Generalizing Computability Theory to Abstract Algebras
title_sort Generalizing Computability Theory to Abstract Algebras
author_id_str_mv 431b3060563ed44cc68c7056ece2f85e
author_id_fullname_str_mv 431b3060563ed44cc68c7056ece2f85e_***_John Tucker
author John Tucker
author2 J. V. Tucker
J. I. Zucker
John Tucker
format Book chapter
container_title Turing’s Revolution
container_start_page 127
publishDate 2016
institution Swansea University
isbn 978-3-319-22156-4
doi_str_mv 10.1007/978-3-319-22156-4_5
publisher Bikhauser/Springer
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
url http://link.springer.com/chapter/10.1007/978-3-319-22156-4_5
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description We present a survey of our work over the last four decades on generalizations of computability theory to many-sorted algebras. The following topics are discussed, among others: (1) abstract v concrete models of computation for such algebras; (2) computability and continuity, and the use of many-sorted topological partial algebras, containing the reals; (3) comparisons between various equivalent and distinct models of computability; and(4) generalized Church-Turing theses.
published_date 2016-01-21T03:37:38Z
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