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Rankable distributions do not provide harder instances than uniform distributions

  • Session 7B: Complexity Theory
  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 959))

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Abstract

We show that polynomially rankable distributions, proposed in [RS93], do not provide harder instances than uniform distributions for NP problems. In particular, we show that if Levin's randomized tiling problem is solvable in polynomial time on average, then every NP problem under any p-rankable distribution is solvable in average polynomial time with respect to rankability. One of the motivations for polynomially rankable distributions was to get average-case hierarchies, and we present a reasonably tight hierarchy result for average-case complexity classes under p-time computable distributions.

Supported in part by NSF under grant CCR-9503601.

Supported in part by NSF under grants CCR-9396331 and CCR-9424164.

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Author information

Authors and Affiliations

  1. Div. of Math & Computer Science, Northeast Missouri State Univ., 63501, Kirksville, MO

    Jay Belanger

  2. Dept. of Mathematical Sciences, Univ. of North Carolina at Greensboro, 27412, Greensboro, NC

    Jie Wang

Authors
  1. Jay Belanger
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  2. Jie Wang
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Ding-Zhu Du Ming Li

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© 1995 Springer-Verlag Berlin Heidelberg

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Belanger, J., Wang, J. (1995). Rankable distributions do not provide harder instances than uniform distributions. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030860

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  • DOI: https://doi.org/10.1007/BFb0030860

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60216-3

  • Online ISBN: 978-3-540-44733-7

  • eBook Packages: Springer Book Archive

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