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Generalizing Computability Theory to Abstract Algebras
J. V. Tucker,
J. I. Zucker,
John Tucker 
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 |
|---|---|
| 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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| 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-sorted topological partial algebras, containing the reals; (3) comparisons between various equivalent and distinct models of computability; and(4) generalized Church-Turing theses. |
|---|---|
| Keywords: |
Computability and continuity, Computability on abstract structures, Computability on the reals, Generalized church-turing thesis, Generalized computability |
| College: |
Faculty of Science and Engineering |
| Start Page: |
127 |
| End Page: |
160 |