computational complexity

, Volume 3, Issue 2, pp 186–205 | Cite as

Relativized isomorphisms of NP-complete sets

  • Judy Goldsmith
  • Deborah Joseph


In this paper, we present several results about collapsing and non-collapsing degrees ofNP-complete sets. The first, a relativized collapsing result, is interesting because it is the strongest known constructive approximation to a relativization of Berman and Hartmanis' 1977 conjecture that all ≤ m P -complete sets forNP arep-isomorphic. In addition, the collapsing result explores new territory in oracle construction, particularly in combining overlapping and apparently incompatible coding and diagonalizing techniques. We also present non-collapsing results, which are notable for their technical simplicity, and which rely on no unproven assumptions such as one-way functions. The basic technique developed in these non-collapsing constructions is surprisingly robust, and can be combined with many different oracle constructions.

Key words

complexity classes isomorphisms NP-completeness collapsing degrees relativized computation sparse oracles 

Subject classifications



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Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • Judy Goldsmith
    • 1
  • Deborah Joseph
    • 2
  1. 1.Department of Computer ScienceUniversity of ManitobaWinnipegCANADA
  2. 2.Department of Computer SciencesUniversity of Wisconsin-MadisonMadisonUSA

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