NP - sets are Co - NP - immune Relative to aRandom

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

We prove that the class NP has Co-NP-immune sets and the class Co-NP has NP-immune sets relative to a random oracle.

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

Relationships between NP-sets, Co-NP-sets, and P-sets relative to random oracles

In the present paper we prove that relative to random oracle A (with respect to the uniform measure) the following three assertions hold: (1) there is a pair of disjoint NP A-sets which are separable by no P A-set, (2) there is a pair of disjoint Co-NP A-sets which are separable by no P A-set and (3) there is an innnite Co-NP A-set having no innnite NP A-subset

Oracle Separation of Complexity Classes and Lower Bounds for Perceptrons Solving Separation Problems

In the rst part of the paper we prove that, relative to a random oracle, the class NP has innnite sets having no innnite Co-NP-subsets (Co-NP-immune sets). In the second part we prove that perceptrons separating Boolean matrices in which each row has a one from matrices in which many rows (say 99% of them) have no ones must have large size or large order. This result partially strengthens one-i...

Almost Weakly 2-Generic Sets

There is a family of questions in relativized complexity theory|weak analogs of the Friedberg Jump-Inversion Theorem|that are resolved by 1-generic sets but which cannot be resolved by essentially any weaker notion of genericity. This paper deenes aw2-generic sets, i.e., sets which meet every dense set of strings that is r.e. in some incomplete r.e. set. Aw2-generic sets are very close to 1-gen...