computational complexity

, Volume 4, Issue 2, pp 158–174 | Cite as

The power of adaptiveness and additional queries in random-self-reductions

  • Joan Feigenbaum
  • Lance Fortnow
  • Carsten Lund
  • Daniel Spielman
Article

Abstract

We study random-self-reductions from a structural complexity-theoretic point of view. Specifically, we look at relationships between adaptive and nonadaptive random-self-reductions. We also look at what happens to random-self-reductions if we restrict the number of queries they are allowed to make. We show the following results:
  • ∘ There exist sets that are adaptively random-self-reducible but not nonadaptively random-self-reducible. Under plausible assumptions, there exist such sets inNP.

  • ∘ There exists a function that has a nonadaptive (k(n)+1)-random-self-reduction but does not have an adaptivek(n)-random-self-reduction.

  • ∘ Forany countable class of functionsC andany unbounded functionk(n), there exists a function that is nonadaptivelyk(n)-uniformly-random-self-reducible but is not inC/poly. This should be contrasted with Feigenbaum, Kannan, and Nisan's theorem that all nonadaptively 2-uniformly-random-self-reducible sets are inNP/poly.

Key words

Adaptiveness random-self-reducibility 

Subject classifications

68Q15 

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Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Joan Feigenbaum
    • 1
  • Lance Fortnow
    • 2
  • Carsten Lund
    • 1
  • Daniel Spielman
    • 3
  1. 1.AT&T Bell LaboratoriesMurray HillUSA
  2. 2.Computer Science DepartmentUniversity of ChicagoChicagoUSA
  3. 3.Mathematics DepartmentMassachusetts Institute of TechnologyCambridgeUSA

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