Nearly optimal language compression using extractors

  • Lance Fortnow
  • Sophie Laplante
Complexity I

DOI: 10.1007/BFb0028551

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1373)
Cite this paper as:
Fortnow L., Laplante S. (1998) Nearly optimal language compression using extractors. In: Morvan M., Meinel C., Krob D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg

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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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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