The Isomorphism Conjecture Holds and One-way Functions Exist Relative to an Oracle (1994)
| Venue: | Journal of Computer and System Sciences |
| Citations: | 9 - 2 self |
BibTeX
@ARTICLE{Rogers94theisomorphism,
author = {John Rogers},
title = {The Isomorphism Conjecture Holds and One-way Functions Exist Relative to an Oracle},
journal = {Journal of Computer and System Sciences},
year = {1994},
volume = {54},
pages = {90--101}
}
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Abstract
In this paper we demonstrate an oracle relative to which there are one-way functions but every paddable 1-li-degree collapses to an isomorphism type, thus yielding a relativized failure of the Joseph-Young Conjecture (JYC) [JY85]. We then use this result to construct an oracle relative to which the Isomorphism Conjecture (IC) is true but one-way functions exist, which answers an open question of Fenner, Fortnow, and Kurtz [FFK92]. Thus, there are now relativizations realizing every one of the four possible states of affairs between the IC and the existence of one-way functions. 1 Introduction Berman and Hartmanis [BH76, BH77] showed that if two languages A and B are equivalent to one another under polynomial-time many-to-one reductions and if they are both paddable then they are polynomial-time isomorphic. After surveying all of the then-known NP-complete languages and discovering that each was indeed paddable, they posed: The Isomorphism Conjecture (IC) Every NP-complete lan...
