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Randomizing reductions of search problems

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1991)

Part of the book series: Lecture Notes in Computer Science ((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.

Partially supported by NSF grant DMR 88-01988.

Partially supported by NSF grant CCR 89-04728 and ONR grant N00014-91-J-11861.

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References

  1. 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.

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  2. 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.

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Author information

Authors and Affiliations

  1. Mathematics Department, University of Michigan, 48109-1003, Ann Arbor, MI, USA

    Andreas Blass

  2. Electrical Engineering and Computer Science Department, University of Michigan, 48109-2122, Ann Arbor, MI, USA

    Yuri Gurevich

Authors
  1. Andreas Blass
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  2. Yuri Gurevich
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Editor information

Somenath Biswas Kesav V. Nori

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© 1991 Springer-Verlag Berlin Heidelberg

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Blass, A., Gurevich, Y. (1991). Randomizing reductions of search problems. In: Biswas, S., Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1991. Lecture Notes in Computer Science, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54967-6_58

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  • DOI: https://doi.org/10.1007/3-540-54967-6_58

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54967-3

  • Online ISBN: 978-3-540-46612-3

  • eBook Packages: Springer Book Archive

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