Discrete transfinite computation

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Abstract

We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have longer tapes than the standard model, or that work on ordinals rather than numbers. We outline the connections between such models and the older theories of recursion in higher types, generalized recursion theory, and recursion on ordinals such as α-recursion. We conclude that, in particular, polynomial time computation on ω-strings is well modelled by several convergent conceptions.
Original languageEnglish
Title of host publicationTuring's Revolution
Subtitle of host publicationThe Impact of His Ideas about Computability
EditorsGiovanni Sommaruga, Thomas Strahm
Place of PublicationBasel
PublisherBirkhäuser Basel
Pages161-185
Number of pages25
ISBN (Electronic)978-3-319-22156-4
ISBN (Print)978-3-319-22156-4
DOIs
Publication statusPublished - 22 Jan 2016

Keywords

  • Turing machine
  • Computability
  • Generalized recursion theory
  • Constructibility

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