Third-order computation and bounded arithmetic (2006)
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by
Alan Skelley
| Venue: | University of Wales Swansea |
| Citations: | 1 - 1 self |
BibTeX
@INPROCEEDINGS{Skelley06third-ordercomputation,
author = {Alan Skelley},
title = {Third-order computation and bounded arithmetic},
booktitle = {University of Wales Swansea},
year = {2006}
}
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Abstract
Abstract. We describe a natural generalization of ordinary computation to a third-order setting and give a function calculus with nice properties and recursion-theoretic characterizations of several large complexity classes. We then present a number of third-order theories of bounded arithmetic whose definable functions are the classes of the EXP-time hierarchy in the third-order setting.
Citations
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| 36 | Some classes of recursive functions - Grzegorczyk - 1953 |
| 35 | Classes of predictably computable functions - Ritchie |
| 25 | Axiomatizations and conservation results for fragments of bounded arithmetic - Buss - 1990 |
| 25 | Theories for Complexity Classes and their Propositional Translations - Cook |
| 19 | Propositional representation of arithmetic proofs - Dowd - 1979 |
| 18 | Provably total functions in bounded arithmetic theories R i 3, U i 2 and V i 2 - Buss, Krajíček, et al. - 1993 |
| 10 | The strength of replacement in weak arithmetic - Cook, Thapen |
| 7 | A Safe Recursion Scheme for Exponential time - Clote - 1996 |
| 7 | A third-order bounded arithmetic theory for PSPACE - Skelley - 2004 |
| 2 | The collapsing hierarchies - Hartmanis - 1987 |
| 2 | Theories and Proof Systems for PSPACE and the EXP-Time Hierarchy - Skelley - 2005 |
