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Fine separation of average time complexity classes

  • Jin -yi Cai
  • Alan L. Selman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)

Abstract

We extend Levin's theory of average polynomial time to arbitrary time-bounds in accordance with the following general principles: (1) It essentially agrees with Levin's notion when applied to polynomial time-bounds. (2) If a language L belongs to DTIME(T(n)), for some time-bound T(n), then every distributional problem (L,μ) is T on the μ-average. (3) If L does not belong to DTIME(T(n)) almost everywhere, then no distributional problem (L, μ) is T on the μ-average.

We present hierarchy theorems for average-case complexity, for arbitrary time-bounds, that are as tight as the well-known Hartmanis-Stearns [HS65] hierarchy theorem for deterministic complexity. As a consequence, for every time-bound T(n), there are distributional problems (L, μ) that can be solved using only a slight increase in time but that cannot be solved on the μ-average in time T(n).

Keywords

Polynomial Time Turing Machine Complexity Class Time Bound Distributional Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Jin -yi Cai
    • 1
  • Alan L. Selman
    • 1
  1. 1.Department of Computer ScienceState University of New York at BuffaloBuffalo

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