A New Characterization of Mehlhorn's Polynomial Time Functionals (Extended Abstract) (1991)
| Venue: | PROCEEDINGS OF THE 32ND ANNUAL IEEE SYMPOSIUM FOUNDATIONS OF COMPUTER SCIENCE |
| Citations: | 6 - 1 self |
BibTeX
@INPROCEEDINGS{Kapron91anew,
author = {Bruce Kapron and Stephen A. Cook},
title = {A New Characterization of Mehlhorn's Polynomial Time Functionals (Extended Abstract)},
booktitle = {PROCEEDINGS OF THE 32ND ANNUAL IEEE SYMPOSIUM FOUNDATIONS OF COMPUTER SCIENCE},
year = {1991},
pages = {342--347},
publisher = {}
}
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Abstract
A type 1 function is a total mapping from N to N. We will denote the set of all such functions by N N. A type 2 functional is a total mapping from ( N N) k \Theta N l to N, for some k; l. More specifically, we will call a mapping of this sort a functional with rank (k; l). For type 1 functions, there is a well established notion of computational feasibility. Namely a function is feasible if it is computable in polynomial time on a Turing machine. More specifically, a function f is poly time if there is a TM M and a polynomial p such that for all x, M with input x computes f(x) and runs in time p(n), where n = jxj, and for x 2 N, jxj denotes the length of the binary notation of x, that is dlog(x + 1)e. This notion of f...
Citations
| 129 | The intrinsic computational difficulty of functions - Cobham - 1964 |
| 79 | Functional interpretations of feasibly constructive arithmetic - Cook, Urquhart - 1993 |
| 30 | Computability and complexity of higher type functions. Logic from computer science - Cook - 1989 |
| 29 | Polynomial and abstract subrecursive classes - Mehlhorn - 1974 |
| 27 | Characterizations of the basic feasible functions of finite type - Cook, Kapron - 1990 |
| 14 | Type two computational complexity - Constable - 1973 |
| 10 | Feasible computation in higher types - Kapron - 1991 |
| 9 | Complexity for type2 relations. Notre Dame - Townsend - 1990 |
| 1 | Iterated recursion is PV ! - definable. Manuscript - Cook - 1989 |
