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 language | English |
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Title of host publication | Turing's Revolution |
Subtitle of host publication | The Impact of His Ideas about Computability |
Editors | Giovanni Sommaruga, Thomas Strahm |
Place of Publication | Basel |
Publisher | Birkhäuser Basel |
Pages | 161-185 |
Number of pages | 25 |
ISBN (Electronic) | 978-3-319-22156-4 |
ISBN (Print) | 978-3-319-22156-4 |
DOIs | |
Publication status | Published - 22 Jan 2016 |
Keywords
- Turing machine
- Computability
- Generalized recursion theory
- Constructibility