Sparse Hard Sets for P

  • Dieter van Melkebeek
  • Mitsunori Ogihara

Abstract

Sparse hard sets for complexity classes has been a central topic for two decades. The area is motivated by the desire to clarify relationships between completeness/hardness and density of languages and studies the existence of sparse complete/hard sets for various complexity classes under various reducibilities. Very recently, we have seen remarkable progress in this area for low-level complexity classes. In particular, the Hartmanis’ sparseness conjectures for P and NL have been resolved. This article overviews the history of sparse hard set problems and exposes some of the recent results.

Keywords

Suffix Berman Hemas 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Dieter van Melkebeek
    • 1
  • Mitsunori Ogihara
    • 2
  1. 1.Department of Computer ScienceUniversity of ChicagoChicagoUSA
  2. 2.Department of Computer ScienceUniversity of RochesterRochesterUSA

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