Authors: Richard Beigel, Martin Kummer, and Frank Stephan

Abstract: 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 n^o(1)-tt reductions is p-superterse unless P = NP. In particular no p-selective set is NP-hard under polynomial-time n^o(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 for 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.

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