On the Error Parameter of Dispersers

  • Ronen Gradwohl
  • Guy Kindler
  • Omer Reingold
  • Amnon Ta-Shma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3624)


Optimal dispersers have better dependence on the error than optimal extractors. In this paper we give explicit disperser constructions that beat the best possible extractors in some parameters. Our constructions are not strong, but we show that having such explicit strong constructions implies a solution to the Ramsey graph construction problem.


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  1. 1.
    Alon, N., Bruck, J., Naor, J., Naor, M., Roth, R.: Construction of asymptotically good, lowrate error-correcting codes through pseudo-random graphs. Transactions on Information Theory 38, 509–516 (1992)CrossRefGoogle Scholar
  2. 2.
    Barak, B., Kindler, G., Shaltiel, R., Sudakov, B., Wigderson, A.: Simulating independence: New constructions of condensers, Ramsey graphs, dispersers, and extractors. In: 37th STOC (2005)Google Scholar
  3. 3.
    Cohen, A., Wigderson, A.: Dispersers, deterministic amplification, and weak random sources. In: Proc. of 30th FOCS, pp. 14–19 (1989)Google Scholar
  4. 4.
    Goldreich, O., Wigderson, A.: Tiny families of functions with random properties: a quality-size trade-off for hashing. Random Structures and Algorithms 11, 4 (1997)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Kahale, N.: Better expansion for Ramanujan graphs. In: 33rd FOCS, pp. 398–404 (1992)Google Scholar
  6. 6.
    Lubotzky, A., Phillips, R., Sarnak, P.: Explicit expanders and the Ramanujan conjectures. In: 18th STOC, pp. 240–246 (1986)Google Scholar
  7. 7.
    Nisan, N., Ta-Shma, A.: Extracting randomness: A survey and new constructions. Journal of Computer and System Sciences 58(1), 148–173 (1999)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Nisan, N., Zuckerman, D.: More deterministic simulation in logspace. In: 25th STOC, pp. 235–244 (1993)Google Scholar
  9. 9.
    Raz, R.: Extractors with weak random seeds. In: 37th STOC (2005)Google Scholar
  10. 10.
    Radhakrishnan, J., Ta-Shma, A.: Tight bounds for depth-two superconcentrators. In: 38th FOCS, Miami Beach, Florida, October 20-22, pp. 585–594. IEEE, Los Alamitos (1997)Google Scholar
  11. 11.
    Raz, R., Reingold, O., Vadhan, S.: Error reduction for extractors. In: 40th FOCS. IEEE, Los Alamitos (1999)Google Scholar
  12. 12.
    Reingold, O., Vadhan, S., Wigderson, A.: Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors. In: Proc. 41st FOCS, pp. 3–13 (2000)Google Scholar
  13. 13.
    Sipser, M.: Expanders, randomness, or time versus space. Journal of Computer and System Sciences 36(3), 379–383 (1988)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Srinivasan, A., Zuckerman, D.: Computing with very weak random sources. In: 35th FOCS, pp. 264–275 (1994)Google Scholar
  15. 15.
    Ta-Shma, A.: Almost optimal dispersers. In: 30th STOC, Dallas, TX, May 1998, pp. 196–202. ACM Press, New York (1998)Google Scholar
  16. 16.
    Ta-Shma, A., Umans, C., Zuckerman, D.: Loss-less condensers, unbalanced expanders, and extractors. In: Proc. 33rd STOC, pp. 143–152 (2001)Google Scholar
  17. 17.
    Ta-Shma, A., Zuckerman, D.: Personal communicationGoogle Scholar
  18. 18.
    Zuckerman, D.: General weak random sources. In: 31st FOCS (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ronen Gradwohl
    • 1
  • Guy Kindler
    • 2
  • Omer Reingold
    • 1
  • Amnon Ta-Shma
    • 3
  1. 1.Department of Computer Science and Applied MathWeizmann Institute of Science 
  2. 2.Institute for Advanced StudyPrinceton
  3. 3.School of Computer ScienceTel-Aviv University 

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