On Characterizations of Randomized Computation Using Plain Kolmogorov Complexity

  • Shuichi Hirahara
  • Akitoshi Kawamura
Conference paper

DOI: 10.1007/978-3-662-44465-8_30

Volume 8635 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Hirahara S., Kawamura A. (2014) On Characterizations of Randomized Computation Using Plain Kolmogorov Complexity. In: Csuhaj-Varjú E., Dietzfelbinger M., Ésik Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg

Abstract

Allender, Friedman, and Gasarch recently proved an upper bound of pspace for the class DTTRK 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 DTTRK 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 DTTRC defined by plain Kolmogorov randomness. In this paper, we provide further evidence for these conjectures. First, we show that the time-bounded analogue of DTTRC sits between BPP and pspace ∩ P/poly. Next, we show that the class DTTRC, α obtained from DTTRC 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.

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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