Note on the P =?NP Problem Relativized

Abstract:

      The P =?NP problem relativized can have two opposite results with the difference of oracle sets. In this paper, we get the results as follows:1. There exists an infinite series of sets S₁,S₂,…, whose complexity is strictly in-creasing, and if they become oracles, they can make the P =?NP and P ≠NP relativized alternately.2. There exists recursive oracle A out of NP such that P = NP equals P^A= NP^A.