Much structural work on NP-complete sets has exploited SAT′s d-self-reducibility. In this paper, we exploit the additional fact that SAT is a d-cylinder to show that NP-complete sets are p-superterse unless P = NP. In fact, every set that is NP-hard under polynomial-time no(1)-tt reductions is p-superterse unless P = NP. In particular, no p-selective set is NP-hard under polynomial-time no(1)-tt reductions unless P = NP. In addition, no easily countable set is NP-hard under Turing reductions unless P = NP. Self-reducibility does not seem to suffice far our main result: in a relativized world, we construct a d-self-reducible set in NP − P that is polynomial-time 2-tt reducible to a p-selective set.
