On completeness under random reductions

The authors study the notion of completeness under random reductions and explore how that depends on the type and success probability of the reduction. They obtain absolute separations between completeness notions under various random reductions and between random reductions and deterministic reductions. These separations are obtained in appropriately high complexity classes where these questions do not have contradictory relativizations. The results show that the notion of completeness under random reductions is sensitive to very small changes in success probability