Comparing Reductions to NP-Complete Sets

  • John M. Hitchcock
  • A. Pavan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)


Under the assumption that NP does not have p-measure 0, we investigate reductions to NP-complete sets and prove the following:

  1. 1

    Adaptive reductions are more powerful than nonadaptive reductions: there is a problem that is Turing-complete for NP but not truth-table-complete.

  2. 2

    Strong nondeterministic reductions are more powerful than deterministic reductions: there is a problem that is SNP-complete for NP but not Turing-complete.

  3. 3

    Every problem that is many-one complete for NP is complete under length-increasing reductions that are computed by polynomial-size circuits.

The first item solves one of Lutz and Mayordomo’s “Twelve Problems in Resource-Bounded Measure” (1999). We also show that every problem that is complete for NE is complete under one-to-one, length-increasing reductions that are computed by polynomial-size circuits.


Query Answer Turing Reduction Adaptive Reduction Oracle Turing Machine Completeness Notion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • John M. Hitchcock
    • 1
  • A. Pavan
    • 2
  1. 1.Department of Computer ScienceUniversity of Wyoming 
  2. 2.Department of Computer ScienceIowa State University 

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