P-Selective Sets, Tally Languages, and the Behavior of Polynomial Time Reducibilities on NP

@inproceedings{Selman1979PSelectiveST,
  title={P-Selective Sets, Tally Languages, and the Behavior of Polynomial Time Reducibilities on NP},
  author={Alan L. Selman},
  booktitle={ICALP},
  year={1979}
}
  • A. Selman
  • Published in ICALP 16 July 1979
  • Mathematics, Computer Science
The notion of p-selective sets, and tally languages, are used to study polynomial time reducibilities on NP. P-selectivity has the property that a set A belongs to the class P if and only if both A NP A and A is p-selective. We prove that for m every tally language set in NP there exists a polynomial time equivalent set in NP that is p-selective. From this result it follows that if NEXT ~ DEXT , then polynomial time Turing and many-one reducibilities differ on NP. 
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  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1983
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Approximable sets
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In a relativized world, a d-self-reducible set in NP-P is constructed that is polynomial-time 2-tt reducible to a p-selective set, and no easily countable set is NP-hard under Turing reductions unless P=NP. Expand
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  • A. Selman
  • Computer Science, Mathematics
  • Inf. Control.
  • 1982
TLDR
The structure of NP <~-degrees is similar to the one of r, and the reducibilities formulated by Cook (1971) and Karp (1973) are just the restrictions to polynomial time of Turing and many-one reducibility, respectively. Expand
Approximable Sets Universitt at Karlsruhe
Much structural work on NP-complete sets has exploited SAT's d-self-reduci-bility. In this paper we exploit the additional fact that SAT is a d-cylinder to show that NP-complete sets are p-superterseExpand
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