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Sparse Hard Sets for P

In: Advances in Algorithms, Languages, and Complexity

Author

Listed:
  • Dieter van Melkebeek

    (University of Chicago, Department of Computer Science)

  • Mitsunori Ogihara

    (University of Rochester, Department of Computer Science)

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.

Suggested Citation

  • Dieter van Melkebeek & Mitsunori Ogihara, 1997. "Sparse Hard Sets for P," Springer Books, in: Ding-Zhu Du & Ker-I Ko (ed.), Advances in Algorithms, Languages, and Complexity, pages 191-208, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3394-4_10
    DOI: 10.1007/978-1-4613-3394-4_10
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