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Banishing robust Turing completeness

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Logical Foundations of Computer Science — Tver '92 (LFCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 620))

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Abstract

This paper shows that “promise classes” are so fragilely structured that they do not robustly possess Turing-hard sets even in classes far larger than themselves. We show that FewP does not robustly possess Turing-hard sets for UP ∩ coUP and IP ∩ coIP does not robustly possess Turing-hard sets for ZPP. It follows that ZPP, R, coR, UP ∩ coUP, UP, FewP ∩ coFewP, FewP, and IP ∩ coIP do not robustly possess Turing complete sets. This both resolves open questions of whether promise classes lacking robust downward closure under Turing reductions (e.g., R, UP, FewP) might robustly have Turing complete sets, and extends the range of classes known not to robustly contain many-one complete sets.

Some of these results were reported at the Symposium on Mathematical Foundations of Computer Science, Carlsbad, Czechoslovakia, September, 1988.

Supported in part by a Hewlett-Packard Corporation equipment grant and the National Science Foundation under grant CCR-8809174/CCR-8996198 and Presidential Young Investigator Award CCR-8957604.

Supported by National Science Foundation grant CCR-8320136 to the University of Rochester.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Rochester, 14627, Rochester, New York

    Lane A. Hemachandra

  2. Department of Computer and Information Sciences, University of Delaware, 19716, Newark, DE

    Sanjay Jain

  3. Department of Mathematical Logic, Moscow State University, 119899, Moscow, Russia

    Nikolai K. Vereshchagin

Authors
  1. Lane A. Hemachandra
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  2. Sanjay Jain
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  3. Nikolai K. Vereshchagin
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Editor information

Anil Nerode Mikhail Taitslin

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© 1992 Springer-Verlag Berlin Heidelberg

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Hemachandra, L.A., Jain, S., Vereshchagin, N.K. (1992). Banishing robust Turing completeness. In: Nerode, A., Taitslin, M. (eds) Logical Foundations of Computer Science — Tver '92. LFCS 1992. Lecture Notes in Computer Science, vol 620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023873

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  • DOI: https://doi.org/10.1007/BFb0023873

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  • Print ISBN: 978-3-540-55707-4

  • Online ISBN: 978-3-540-47276-6

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