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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
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© 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


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