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Reductions and convergence rates of average time

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Computing and Combinatorics (COCOON 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1090))

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Abstract

Using a fast convergence rate to measure computation time on average has recently been investigated [CS95a], which modifies the notion of T-time on average [BCGL92]. This modification admits an average-case time hierarchy which is independent of distributions and is as tight as the Hartmanis-Sterns hierarchy for the worst-case deterministic time [HS65]. Various notions of reductions, defined by Levin [Lev86] and others, have played a central role in studying average-case complexity. However, unless the class of admissible distributions is restricted, these notions of reductions cannot be applied to the modified definition. In particular, we show that under the modified definition, there exists a problem which is not computable in average polynomial time, but is efficiently reducible to one that is. We hope that this observation can further stimulate research on finding suitable reductions in this new line of investigation.

Supported in part by NSF under grant CCR-9503601.

Supported in part by NSF under grant CCR-9424164.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of North Carolina at Greensboro, 27412, Greensboro, NC, USA

    Jie Wang

  2. Division of Mathematics and Computer Science, Northeast Missouri State University, 63501, Kirksville, MO, USA

    Jay Belanger

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  1. Jay Belanger
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  2. Jie Wang
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Correspondence to Jie Wang .

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Jin-Yi Cai Chak Kuen Wong

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© 1996 Springer-Verlag Berlin Heidelberg

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Belanger, J., Wang, J. (1996). Reductions and convergence rates of average time. In: Cai, JY., Wong, C.K. (eds) Computing and Combinatorics. COCOON 1996. Lecture Notes in Computer Science, vol 1090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61332-3_164

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  • DOI: https://doi.org/10.1007/3-540-61332-3_164

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61332-9

  • Online ISBN: 978-3-540-68461-9

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