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Approximable sets

Author: Richard Beigel; Martin Kummer; Frank Stephan
Publisher: Amsterdam, the Netherlands : Centrum voor Wiskunde en Informatica, [1993]
Series: Report (Centrum voor Wiskunde en Informatica (Amsterdam, Netherlands). Computer Science/Dept. of Algorithmics and Architecture, CS-R9372.
Edition/Format:   Book : English
Database:WorldCat
Summary:
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[superscript o(1)]-tt reductions is p-superterse unless P = NP. In particular no p-selective set is NP-hard under polynomial-time  Read more...
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Document Type: Book
All Authors / Contributors: Richard Beigel; Martin Kummer; Frank Stephan
OCLC Number: 31639680
Notes: "December 1993."
Description: 15 pages ; 29 cm.
Series Title: Report (Centrum voor Wiskunde en Informatica (Amsterdam, Netherlands). Computer Science/Dept. of Algorithmics and Architecture, CS-R9372.
Responsibility: R. Beigel, M. Kummer, F. Stephan.

Abstract:

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[superscript o(1)]-tt reductions is p-superterse unless P = NP. In particular no p-selective set is NP-hard under polynomial-time n[superscript 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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