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Generalizing Computability Theory to Abstract Algebras
Turing’s Revolution, Pages: 127 - 160
Swansea University Author: John Tucker
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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...
Published in: | Turing’s Revolution |
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ISBN: | 978-3-319-22156-4 |
Published: |
Basel
Bikhauser/Springer
2016
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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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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 |
|
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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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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1 |
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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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1763751660344049664 |
score |
11.0299 |