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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1993: STACS 93 pp 185–195Cite as

Defying upward and downward separation

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 665))

Abstract

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.

Research supported in part by the National Science Foundation under grant CCR-8957604. A full version is available upon request to lane@cs.rochester.edu.

Work done in part while visiting Friedrich Schiller Universität Jena and Universität Ulm.

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Author information

Author notes

  1. Sudhir K. Jha

    Present address: Design Technology, SC3-38, Intel Corporation, 2880 Northwestern Parkway, 95052, Santa Clara, CA

Authors and Affiliations

  1. Department of Computer Science, University of Rochester, 14627, Rochester, NY

    Lane A. Hemachandra & Sudhir K. Jha

Authors
  1. Lane A. Hemachandra
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  2. Sudhir K. Jha
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Editor information

P. Enjalbert A. Finkel K. W. Wagner

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© 1993 Springer-Verlag Berlin Heidelberg

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Hemachandra, L.A., Jha, S.K. (1993). Defying upward and downward separation. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_21

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  • DOI: https://doi.org/10.1007/3-540-56503-5_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56503-1

  • Online ISBN: 978-3-540-47574-3

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