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Optimal Proof Systems and Sparse Sets

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STACS 2000 (STACS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1770))

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Abstract

We exhibit a relativized world where NP ∩ SPARSE has no complete sets. This gives the first relativized world where no optimal proof systems exist.

We also examine under what reductions NP ∩ SPARSE can have complete sets. We show a close connection between these issues and reductions from sparse to tally sets. We also consider the question as to whether the NP ∩ SPARSE languages have a computable enumeration.

Several proofs have been omitted to conserve space. A full version can be found at http://www.neci.nj.nec.com/homepages/fortnow/papers.

Supported in part by NSF grants CCR-9501794 and CCR-9996310.

Supported in part by NSF grant CCR-9732922.

Supported in part by NSF grant CCR-9732922.

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Author information

Author notes

  1. Lance Fortnow

    Present address: NEC Research, 4 Independence Way, Princeton, NJ, 08540

  2. Dieter van Melkebeek

    Present address: DIMACS Center, Rutgers University, 96 Frelinghuysen Road, Piscataway, NJ, 08854

Authors and Affiliations

  1. CWI, INS4, P.O. Box 94079, 1090 GB, Amsterdam, The Netherlands

    Harry Buhrman

  2. Department of Computer Science, The University of South Carolina, Columbia, SC, 29208

    Steve Fenner

  3. University of Chicago, Chicago

    Lance Fortnow

  4. University of Chicago and DIMACS, Chicago

    Dieter van Melkebeek

Authors
  1. Harry Buhrman
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  2. Steve Fenner
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  3. Lance Fortnow
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  4. Dieter van Melkebeek
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dept. of Theoretical Computer Science, Universität Dresden, 01062, Dresden, Germany

    Horst Reichel

  2. Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA, 59655, Villeneuve d’ASCQ Cedex, France

    Sophie Tison

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© 2000 Springer-Verlag Berlin Heidelberg

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Buhrman, H., Fenner, S., Fortnow, L., van Melkebeek, D. (2000). Optimal Proof Systems and Sparse Sets. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_34

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  • DOI: https://doi.org/10.1007/3-540-46541-3_34

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67141-1

  • Online ISBN: 978-3-540-46541-6

  • eBook Packages: Springer Book Archive

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