Nearly optimal language compression using extractors

  • Lance Fortnow
  • Sophie Laplante
Complexity I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1373)

Abstract

We show two sets of results applying the theory of extractors to resource-bounded Kolmogorov complexity:
  • - Most strings in easy sets have nearly optimal polynomial-time CD complexity. This extends work of Sipser [Sip83] and Buhrman and Fortnow [BF97].

  • - We use extractors to extract the randomness of strings. In particular we show how to get from an arbitrary string, an incompressible string which encodes almost as much polynomial-time CND complexity as the original string.

Topics

Computational and structural complexity Kolmogorov complexity 

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References

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Lance Fortnow
    • 1
  • Sophie Laplante
    • 2
  1. 1.Department of Computer ScienceUniversity of ChicagoChicago
  2. 2.Laboratoire de Recherche en Informatique, Bât.Orsay CedexFrance

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