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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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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