### 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 language | English |
---|---|

Title of host publication | Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings |

Publisher | Springer Verlag |

Pages | 348-359 |

Number of pages | 12 |

Edition | PART 2 |

ISBN (Print) | 9783662444641 |

DOIs | |

Publication status | Published - Jan 1 2014 |

Event | 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014 - Budapest, Hungary Duration: Aug 25 2014 → Aug 29 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Number | PART 2 |

Volume | 8635 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014 |
---|---|

Country | Hungary |

City | Budapest |

Period | 8/25/14 → 8/29/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - On characterizations of randomized computation using plain Kolmogorov complexity

AU - Hirahara, Shuichi

AU - Kawamura, Akitoshi

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84906264560&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906264560&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-44465-8_30

DO - 10.1007/978-3-662-44465-8_30

M3 - Conference contribution

AN - SCOPUS:84906264560

SN - 9783662444641

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 348

EP - 359

BT - Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings

PB - Springer Verlag

ER -