Computation and hypercomputation
File(s)
Published version
Author(s)
Powell, Andrew
Type
Journal Article
Abstract
This paper shows some of the differences and similarities between computation and hypercomputation, the similarities relating to the complexity of propositional computation and the differences being the propositions that can be decided computationally or hypercomputationally. The methods used are ordinal Turing machines with infinitely long programs and diagonalization out of computing complexity classes. The main results are the characterization of inequalities of run time complexities of serial, indeterministic serial and parallel computers and hypercomputers and the specification of a hierarchy of hypercomputers that can hypercompute the truths of all propositions in the standard class model of set theory, the von Neumann hierarchy of pure sets.
Editor(s)
Massouros, Christos G
Date Issued
2022-03-20
Date Acceptance
2022-03-15
Citation
Mathematics, 2022, 10 (6), pp.1-16
ISSN
2227-7390
Publisher
MDPI
Start Page
1
End Page
16
Journal / Book Title
Mathematics
Volume
10
Issue
6
Copyright Statement
© 2022 by the author.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000774106300001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Mathematics
computation
diagonalization
hypercomputation
recursion theory
von Neumann hierarchy of pure sets
NOT-EQUAL NP
TIME
MACHINES
Publication Status
Published
Article Number
ARTN 997
Date Publish Online
2022-03-20