On Characterizations of Randomized Computation Using Plain Kolmogorov Complexity

  • Shuichi Hirahara
  • Akitoshi Kawamura
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8635)


Allender, Friedman, and Gasarch recently proved an upper bound of pspace for the class DTTR K of decidable languages that are polynomial-time truth-table reducible to the set of prefix-free Kolmogorov-random strings regardless of the universal machine used in the definition of Kolmogorov complexity. It is conjectured that DTTR K in fact lies closer to its lower bound BPP established earlier by Buhrman, Fortnow, Koucký, and Loff. It is also conjectured that we have similar bounds for the analogous class DTTR C defined by plain Kolmogorov randomness. In this paper, we provide further evidence for these conjectures. First, we show that the time-bounded analogue of DTTR C sits between BPP and pspace ∩ P/poly. Next, we show that the class DTTR C, α obtained from DTTR C by imposing a restriction on the reduction lies between BPP and pspace. Finally, we show that the class P/R\(^{=log}_{c}\) obtained by further restricting the reduction to ask queries of logarithmic length lies between BPP and \(\Sigma^{p}_{2} \cap\) P/poly.


Turing Machine Initial Segment Winning Strategy Full Version Kolmogorov Complexity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Shuichi Hirahara
    • 1
  • Akitoshi Kawamura
    • 1
  1. 1.The University of TokyoJapan

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