Parallel computable higher type functionals (Extended Abstract) (1993)
| Venue: | In Proceedings of IEEE 34th Annual Symposium on Foundations of Computer Science, Nov 3--5 |
| Citations: | 4 - 4 self |
BibTeX
@INPROCEEDINGS{Clote93parallelcomputable,
author = {P. Clote and A. Ignatovic and B.M. Kapron},
title = {Parallel computable higher type functionals (Extended Abstract)},
booktitle = {In Proceedings of IEEE 34th Annual Symposium on Foundations of Computer Science, Nov 3--5},
year = {1993},
pages = {72--83}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
) Peter Clote A. Ignjatovic y B. Kapron z 1 Introduction to higher type functionals The primary aim of this paper is to introduce higher type analogues of some familiar parallel complexity classes, and to show that these higher type classes can be characterized in significantly different ways. Recursion-theoretic, proof-theoretic and machine-theoretic characterizations are given for various classes, providing evidence of their naturalness. In this section, we motivate the approach of our work. In proof theory, primitive recursive functionals of higher type were introduced in Godel's Dialectica [13] paper, where they were used to "witness" the truth of arithmetic formulas. For instance, a function f witnesses the formula 8x9y\Phi(x; y), where \Phi is quantifier-free, provided that 8x\Phi(x; f(x)); while a type 2 functional F witnesses the formula 8x9y8u9v\Phi(x; y; u; v), provided that 8x8u\Phi(x; f(x); u; F (x; f(x); u)): Godel's formal system T is a variant of the finit...
