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R SN1−tt (NP) distinguishes robust many-one and Turing completeness

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Algorithms and Complexity (CIAC 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1203))

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Abstract

Do complexity classes have many-one complete sets if and only if they have Turing-complete sets? We prove that there is a relativized world in which a relatively natural complexity class—namely a downward closure of NP, R SN1−tt (NP)—has Turing-complete sets but has no many-one complete sets. In fact, we show that in the same relativized world this class has 2-truth-table complete sets but lacks 1-truth-table complete sets. As part of the groundwork for our result, we prove that R SN1−tt (NP) has many equivalent forms having to do with ordered and parallel access to NP and NP ∩ coNP.

A full version, containing full proofs of all results, can be found as UR-CS-TR-635 at http://www.cs.rochester.edu/trs/.

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

Giancarlo Bongiovanni Daniel Pierre Bovet Giuseppe Di Battista

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© 1997 Springer-Verlag Berlin Heidelberg

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Hemaspaandra, E., Hemaspaandra, L.A., Hempel, H. (1997). R SN1−tt (NP) distinguishes robust many-one and Turing completeness. In: Bongiovanni, G., Bovet, D.P., Di Battista, G. (eds) Algorithms and Complexity. CIAC 1997. Lecture Notes in Computer Science, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62592-5_60

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  • DOI: https://doi.org/10.1007/3-540-62592-5_60

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  • Print ISBN: 978-3-540-62592-6

  • Online ISBN: 978-3-540-68323-0

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