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computational complexity

, Volume 11, Issue 3–4, pp 137–157 | Cite as

Separability and one-way functions

  • Lance Fortnow
  • John D. Rogers
Original Article

Abstract

We settle all relativized questions of the relationships between the following five propositions:
  • P = NP.

  • P = UP.

  • P = NP $\cap$ coNP.

  • All disjoint pairs of NP sets are P-separable.

  • All disjoint pairs of coNP sets are P-separable.

We make the first widespread use of variations of generic oracles to achieve the necessary relativized worlds.

Keywords.

Structural complexity relativization generic oracles 

Mathematics Subject Classification (2000).

68Q15 

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Copyright information

© Birkhäuser-Verlag 2002

Authors and Affiliations

  1. 1.Computer Science DepartmentUniversity of ChicagoChicagoUSA
  2. 2.School of CTIDePaul UniversityChicagoUSA

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