On characterizations of randomized computation using plain Kolmogorov complexity

Shuichi Hirahara, Akitoshi Kawamura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

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 obtained by further restricting the reduction to ask queries of logarithmic length lies between BPP and P/poly.

Original languageEnglish
Title of host publicationMathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings
PublisherSpringer Verlag
Pages348-359
Number of pages12
EditionPART 2
ISBN (Print)9783662444641
DOIs
Publication statusPublished - Jan 1 2014
Externally publishedYes
Event39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014 - Budapest, Hungary
Duration: Aug 25 2014Aug 29 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume8635 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014
CountryHungary
CityBudapest
Period8/25/148/29/14

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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