Defying upward and downward separation

  • Lane A. Hemachandra
  • Sudhir K. Jha
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)


Upward and downward separation results link the collapse of small and large classes, and are a standard tool in complexity theory. We study the limitations of upward and downward separation.

We show that the exponential-time limited nondeterminism hierarchy does not robustly possess downward separation. We show that probabilistic classes do not robustly possess upward separation. Though NP is known [19] to robustly possess upward separation, we show that NP does not robustly possess upward separation with respect to strong (immunity) separation. On the other hand, we provide a structural sufficient condition for upward separation.


Turing Machine Complexity Class SIAM Journal Kolmogorov Complexity Information Processing Letter 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Lane A. Hemachandra
    • 1
  • Sudhir K. Jha
    • 1
  1. 1.Department of Computer ScienceUniversity of RochesterRochester

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