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Randomizing reductions of search problems

Extended abstract
  • Andreas Blass
  • Yuri Gurevich
Invited Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 560)

Abstract

This paper closes a gap in the foundations of the theory of average case complexity. First, we clarify the notion of a (feasible) solution for a search problem and prove its robustness. Second, we give a general and usable notion of many-one randomizing reductions of search problems and prove that it has desirable properties. All reductions of search problems to search problems in the literature on average case complexity can be viewed as such many-one randomizing reductions. This includes those reductions in the literature that use iterations and therefore do not look manyone.

Keywords

Success Probability Random Function Initial Segment Search Problem Random String 
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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References

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    Shai Ben-David, Benny Chor, Oded Goldreich and Michael Luby, “On the Theory of Average Case Complexity”, Symposium on Theory of Computing, ACM, 1989, 204–216.Google Scholar
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    Andreas Blass and Yuri Gurevich, “On the Reduction Theory for Average-Case Complexity”, CSL'90, 4th Workshop on Computer Science Logic (Eds. E. Borger, H. Kleine Buning and M. Richter), Springer LNCS, 1991.Google Scholar
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    Leonid A. Levin, “Average Case Complete Problems”, SIAM Journal of Computing 15(1986), 285–286.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Andreas Blass
    • 1
  • Yuri Gurevich
    • 2
  1. 1.Mathematics DepartmentUniversity of MichiganAnn ArborUSA
  2. 2.Electrical Engineering and Computer Science DepartmentUniversity of MichiganAnn ArborUSA

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