The isomorphism conjecture fails relative to a random oracle

The Isomorphism Conjecture Holds Relative to an Oracle

We introduce symmetric perfect generic sets. These sets vary from the usual generic sets by allowing limited innnite encoding into the oracle. We then show that the Berman-Hartmanis isomorphism conjecture BH77] holds relative to any sp-generic oracle, i.e., for any symmetric perfect generic set A, all NP A-complete sets are polynomial-time isomorphic relative to A. Prior to this work there were...

Circuit Depth Relative to a Random Oracle

Relative to a Random Oracle , NP Is Not

Resource-bounded measure as originated by Lutz is an extension of classical measure theory which provides a probabilistic means of describing the relative sizes of complexity classes. Lutz has proposed the hypothesis that NP does not have p-measure zero, meaning loosely that NP contains a non-negligible subset of exponential time. This hypothesis implies a strong separation of P from NP and is ...

Relative to a Random Oracle, NP is Not Small

Resource-bounded measure as originated by Lutz is an extension of classical measure theory which provides a probabilistic means of describing the relative sizes of complexity classes. Lutz has proposed the hypothesis that NP does not have p-measure zero, meaning loosely that NP contains a non-negligible subset of exponential time. This hypothesis implies a strong separation of P from NP and is ...

The Isomorphism Conjecture for NP

In this article, we survey the arguments and known results for and against the Isomorphism Conjecture.