Generalizing Computability Theory to Abstract Algebras

J. V. Tucker () and J. I. Zucker ()
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J. V. Tucker: Swansea University, Department of Computer Science
J. I. Zucker: McMaster University, Department of Computing and Software

A chapter in Turing’s Revolution, 2015, pp 127-160 from Springer

Abstract: 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; (4) generalized Church-Turing theses.

Keywords: Computability and continuity; Computability on abstract structures; Computability on the reals; Generalized church-turing thesis; Generalized computability (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22156-4_5

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DOI: 10.1007/978-3-319-22156-4_5

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