Sparse sets in NP-P: Exptime versus nexptime

  • Authors:
  • J. Hartmanis;V. Sewelson;N. Immerman

  • Affiliations:
  • -;-;-

  • Venue:
  • STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
  • Year:
  • 1983

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Abstract

This paper investigates the structural properties of sets in NP-P and shows that the computational difficulty of lower density sets in NP depends explicitly on the relations between higher deterministic and nondeterministic time-bounded complexity classes. The paper exploits the recently discovered upward separation method, which shows for example that there exist sparse sets in NP-Pif and only if EXPTIME @@@@ NEXPTIME. In addition, the paper uses relativization techniques to determine logical possibilities, limitations of these proof techniques, and, for the first time, to exhibit structural differences between relativized NP and CoNP.