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Collapsing Hierarchies

  • Uwe Schöning
  • Randall Pruim

Abstract

The polynomial hierarchy can be defined in exact analogy to the arithmetic hierarchy of computability theory, but it is not known if the polynomial hierarchy is a strict hierarchy of language classes. In fact, under certain assumptions about the class NP, this hierarchy “collapses.”

Keywords

Satisfying Assignment Existential Quantifier Output Gate Polynomial Hierarchy Inclusion Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. L.J. Stockmeyer: The polynomial-time hierarchy, Theoretical Computer Science 3 (1977), 1–22.MathSciNetzbMATHCrossRefGoogle Scholar
  2. C. Wrathall: Complete sets and the polynomial-time hierarchy, Theoretical Computer Science 3 (1977), 23–33.MathSciNetzbMATHCrossRefGoogle Scholar
  3. R.M. Karp, R.J. Lipton: Some connections between nonuniform and uniform complexity classes, Proceedings of the 12th Symposium on Theory of Computer Science, ACM, 1980, 302-309.Google Scholar
  4. N.H. Bshouty, R. Cleve, S. Kannan, C. Tamon: Oracles and queries that are sufficient for exact learning, COLT 1994.Google Scholar
  5. Cai, Gundermann, Hartmanis, Hemachandra, Sewelson, Wagner, Wechsung: The Boolean hierarchy I & II, SI AM Journal on Computing 17 (1989), 1232–1252 and 18 (1989), 95–111.MathSciNetCrossRefGoogle Scholar
  6. Kadin: The polynomial hierarchy collapses if the Boolean hierarchy collapses, SI AM Journal on Computing 17 (1988), 1263–1282MathSciNetzbMATHCrossRefGoogle Scholar
  7. R. Chang, J. Kadin: The Boolean hierarchy and the polynomial hierarchy: a closer connection, Proceedings of the Structure in Complexity Theory Conference, IEEE, 1990, 169-178.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Uwe Schöning
    • 1
  • Randall Pruim
    • 2
  1. 1.Abt. Theoretische InformatikUniversität UlmUlmGermany
  2. 2.Dept. of Mathematics and StatisticsCalvin CollegeGrand RapidsUSA

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