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
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

Fingerprint

Kolmogorov Complexity
P-space
Polynomials
Prefix-free
Truth table
Randomness
Polynomial time
Logarithmic
Strings
Query
Lower bound
Upper bound
Restriction
Analogue
Class

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Hirahara, S., & Kawamura, A. (2014). On characterizations of randomized computation using plain Kolmogorov complexity. In Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings (PART 2 ed., pp. 348-359). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8635 LNCS, No. PART 2). Springer Verlag. https://doi.org/10.1007/978-3-662-44465-8_30

On characterizations of randomized computation using plain Kolmogorov complexity. / Hirahara, Shuichi; Kawamura, Akitoshi.

Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings. PART 2. ed. Springer Verlag, 2014. p. 348-359 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8635 LNCS, No. PART 2).

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

Hirahara, S & Kawamura, A 2014, On characterizations of randomized computation using plain Kolmogorov complexity. in Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings. PART 2 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 8635 LNCS, Springer Verlag, pp. 348-359, 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, Budapest, Hungary, 8/25/14. https://doi.org/10.1007/978-3-662-44465-8_30
Hirahara S, Kawamura A. On characterizations of randomized computation using plain Kolmogorov complexity. In Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings. PART 2 ed. Springer Verlag. 2014. p. 348-359. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2). https://doi.org/10.1007/978-3-662-44465-8_30
Hirahara, Shuichi ; Kawamura, Akitoshi. / On characterizations of randomized computation using plain Kolmogorov complexity. Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings. PART 2. ed. Springer Verlag, 2014. pp. 348-359 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2).
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