Skip Navigation


Journal of Logic and Computation Advance Access originally published online on November 13, 2007
Journal of Logic and Computation 2007 17(6):1167-1191; doi:10.1093/logcom/exm040
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
17/6/1167    most recent
exm040v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Skelley, A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Third-Order Computation and Bounded Arithmetic

Alan Skelley *

Mathematical Institute, Academy of Sciences of the Czech Republic, Zitná 25, CZ - 115 67 Praha 1, Czech Republic. E-mail: alan{at}cs.toronto.edu


  Abstract

We describe a natural generalization of ordinary computation to a third-order (i.e. three-sorted) setting. We give a function calculus with nice properties and recursion-theoretic characterizations of several large complexity classes, including classes of functions and predicates from the levels of the exponential-time hierarchy. We then present a number of third-order theories of bounded arithmetic whose definable functions are the classes of the exponential time hierarchy in the third-order setting.

Keywords: Bounded arithmetic; recursion theory; computability; exponential-time hierarchy; computational complexity


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.