No Cover Image

Book Chapter 391 views 17 downloads

Generalizing Computability Theory to Abstract Algebras / J. V. Tucker; J. I. Zucker

Turing’s Revolution, Pages: 127 - 160

Swansea University Author: Tucker, John

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...

Full description

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
Tags: Add Tag
No Tags, Be the first to tag this record!
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: College of Science
Start Page: 127
End Page: 160