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A downward translation in the polynomial hierarchy

  • Structural Complexity II
  • Conference paper
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STACS 97 (STACS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1200))

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Abstract

Downward translation (a.k.a. upward separation) refers to cases where the equality of two larger classes implies the equality of two smaller classes. We provide the first unqualified downward translation result completely within the polynomial hierarchy. In particular, we prove that, for k>2,

$$P^{\sum\nolimits_k^p {[1]} } = P^{\sum\nolimits_k^p {[2]} } \Leftrightarrow \sum _k^p = \Pi _k^p ,$$

where the “[1]” (respectively, “[2]”) denotes that at most one query is (respectively, two queries are) allowed. We also extend this to obtain a more general downward translation result.

A full version of this paper, including proofs of all claims, can be found as University of Rochester Department of Computer Science Technical Report TR-96-630, at http://www.cs.rochester.edu/trs/theory-trs.html.

Supported in part by grant NSF-INT-9513368/DAAD-315-PRO-fo-ab. Work done in part while visiting Friedrich-Schiller-Universitat Jena.

Supported in part by grants NSF-CCR-9322513 and NSF-INT-9513368/DAAD-315-PRO-fo-ab. Work done in part while visiting Friedrich-Schiller-Universitat Jena.

Supported in part by grant NSF-INT-9513368/DAAD-315-PRO-fo-ab.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Le Moyne College, 13214, Syracuse, NY, USA

    Edith Hemaspaandra

  2. Department of Computer Science, University of Rochester, 14627, Rochester, NY, USA

    Lane A. Hemaspaandra

  3. Inst. für Informatik, Friedrich-Schiller-Universität Jena, 07743, Jena, Germany

    Harald Hempel

Authors
  1. Edith Hemaspaandra
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  2. Lane A. Hemaspaandra
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  3. Harald Hempel
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Editor information

Rüdiger Reischuk Michel Morvan

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© 1997 Springer-Verlag Berlin Heidelberg

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Hemaspaandra, E., Hemaspaandra, L.A., Hempel, H. (1997). A downward translation in the polynomial hierarchy. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023469

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  • DOI: https://doi.org/10.1007/BFb0023469

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62616-9

  • Online ISBN: 978-3-540-68342-1

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