Circuit Depth Relative to a Random Oracle

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 ...

Relative to a Random Oracle, P/Poly is not Measurable in EXP

It is shown that, with respect to a random oracle, EXP \ P=poly and EXP ? P=poly do not have resource-bounded measure zero in EXP:

NP-sets are Co-NP-immune Relative to a Random Oracle