A New Characterization Of Type 2 Feasibility (1996)
| Citations: | 35 - 6 self |
BibTeX
@MISC{Cook96anew,
author = {Kapron Cook and S. A. Cook},
title = {A New Characterization Of Type 2 Feasibility},
year = {1996}
}
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Abstract
. K. Mehlhorn introduced a class of polynomial time computable operators in order to study poly time reducibilities between functions. This class is defined using a generalization of A. Cobham's definition of feasibility for type 1 functions to type 2 functionals. Cobham's feasible functions are equivalent to the familiar poly time functions. We generalize this equivalence to type 2 functionals. This requires a definition of the notion `poly time in the length of type 1 inputs'. The proof of this equivalence is not a simple generalization of the proof for type 1 functions; it depends on the fact that Mehlhorn's class is closed under a strong form of simultaneous limited recursion on notation, and requires an analysis of the structure of oracle queries in time bounded computations. Key words. type 2 computability, polynomial time, notational recursion, oracle Turing machine AMS subject classifications. 68Q05,68Q15,03D65,03D20 1. Introduction. A type 1 function is a mapping from N to ...
Citations
| 129 | The intrinsic computational difficulty of functions - Cobham - 1964 |
| 29 | Polynomial and abstract subrecursive classes - Mehlhorn - 1974 |
| 27 | Characterizations of the basic feasible functions of finite type - Cook, Kapron - 1990 |
| 19 | Computational complexity of real functions, Theoret - Ko, Friedman - 1982 |
| 10 | Feasible computation in higher types - Kapron - 1991 |
| 9 | Complexity for type2 relations. Notre Dame - Townsend - 1990 |
| 3 | A new characterization of Mehlhorn's poly time functionals - Kapron, Cook - 1991 |
| 1 | Iterated recursion is PV-definable - Cook - 1989 |
| 1 | c, On Feasibility - Ignjatovi - 1994 |
