Reductions and convergence rates of average time

  • Jay Belanger
  • Jie Wang
Session 9
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1090)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of North Carolina at GreensboroGreensboroUSA
  2. 2.Division of Mathematics and Computer ScienceNortheast Missouri State UniversityKirksvilleUSA

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