Sparse Hard Sets for P

  • Dieter van Melkebeek
  • Mitsunori Ogihara


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.


Complexity Class Satisfying Assignment Boolean Circuit Collision Pair SIGACT News 
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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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