Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Randomizing reductions of search problems

Extended abstract

  • Invited Papers
  • Conference paper
  • First Online:
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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

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.

    Google Scholar 

  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.

    Google Scholar 

  3. Yuri Gurevich, “Average Case Complexity”, J. Computer and System Sciences 42:3, June 1991 (a special issue on FOCS'87), 346–398.

    Article  Google Scholar 

  4. Yuri Gurevich, “Average Case Complexity”, International Colloquium on Automata, Languages and Programming, Springer Lecture Notes in Computer Science 510, 1991, 615–628.

    Google Scholar 

  5. Russel Impagliazzo and Leonid A. Levin, “No Better Ways to Generate Hard NP Instances than Picking Uniformly at Random”, Symposium on Foundations of Computer Science, IEEE Computer Society Press, 1990, 812–821.

    Google Scholar 

  6. Leonid A. Levin, “Average Case Complete Problems”, SIAM Journal of Computing 15(1986), 285–286.

    Article  Google Scholar 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuri Gurevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Somenath Biswas Kesav V. Nori

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54967-3

  • Online ISBN: 978-3-540-46612-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation