Collapsing Hierarchies

  • Uwe Schöning
  • Randall Pruim


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.”


Satisfying Assignment Existential Quantifier Output Gate Polynomial Hierarchy Inclusion Structure 
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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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