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Almost Complete 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 show that there is a set which is almost complete but not complete under polynomial-time many-one (p-m) reductions for the class E of sets computable in deterministic time 2lin. Here a set A in a complexity class C is almost complete for C under some reducibility r if the class of the problems in C which do not r-reduce to A has measure 0 in C in the sense of Lutz’s resource-bounded measure theory. We also show that the almost complete sets for E under polynomial-time bounded one-one length-increasing reductions and truth-table reductions of norm 1 coincide with the almost p-m-complete sets for E. Moreover, we obtain similar results for the class EXP of sets computable in deterministic time 2poly.

Supported by Marie Curie Fellowship ERB-FMBI-CT98-3248.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 294, D-69120, Heidelberg, Germany

    Klaus Ambos-Spies, Wolfgang Merkle & Jan Reimann

  2. Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstr. 39, D-80333, München, Germany

    Sebastiaan A. Terwijn

Authors
  1. Klaus Ambos-Spies
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  2. Wolfgang Merkle
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  3. Jan Reimann
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  4. Sebastiaan A. Terwijn
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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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Ambos-Spies, K., Merkle, W., Reimann, J., Terwijn, S.A. (2000). Almost Complete 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_35

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  • DOI: https://doi.org/10.1007/3-540-46541-3_35

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  • Print ISBN: 978-3-540-67141-1

  • Online ISBN: 978-3-540-46541-6

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