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Separability and one-way functions

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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.

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Authors and Affiliations

  1. Computer Science Department, University of Chicago, Chicago, 60637, IL, USA

    Lance Fortnow

  2. School of CTI, DePaul University, Chicago, 60604, IL, USA

    John D. Rogers

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  1. Lance Fortnow
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  2. John D. Rogers
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Correspondence to Lance Fortnow.

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Fortnow, L., Rogers, J. Separability and one-way functions. comput. complex. 11, 137–157 (2002). https://doi.org/10.1007/s00037-002-0173-4

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  • DOI: https://doi.org/10.1007/s00037-002-0173-4

Keywords.

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