$P\not=NP$ relative to a $P$-complete oracle

Abstract

The $P$ versus $NP$ problem is still unsolved. But there are several oracles with $P$ unequal $NP$ relative to them. Here we will prove, that $P\not=NP$ relative to a $P$-complete oracle. In this paper, we use padding arguments as the proof method. The padding arguments are not bounded by a computable function. Such as we can use methods from computability theory to separate complexity classes.