PP-2010-23:
Barmpalias, George and Sterkenburg, Tom
(2010)
*On the number of infinite sequences with trivial initial segment complexity.*
[Report]

Preview |
Text (Full Text)
PP-2010-23.text.pdf Download (325kB) | Preview |

Text (Abstract)
PP-2010-23.abstract.txt Download (822B) |

## Abstract

The sequences which have trivial prefix-free initial segment

complexity are known as K-trivial sets, and form a cumulative

hierarchy of length ~. We show that the problem of finding the number

of K-trivial sets in the various levels of the hierarchy is

~^0_3. This answers a question of Downey/Miller/Yu (see [DH10, Section

10.1.4]) which also appears in [Nie09, Problem 5.2.16].

We also show the same for the hierarchy of the low for K sequences,

which are the ones that (when used as oracles) do not give shorter

initial segment complexity compared to the computable oracles. In both

cases the classification ~^0_3 is sharp.

Item Type: | Report |
---|---|

Report Nr: | PP-2010-23 |

Series Name: | Prepublication (PP) Series |

Year: | 2010 |

Uncontrolled Keywords: | Kolmogorov Complexity; arithmetical complexity; K-trivial |

Depositing User: | gbarmpa1 |

Date Deposited: | 12 Oct 2016 14:37 |

Last Modified: | 12 Oct 2016 14:37 |

URI: | https://eprints.illc.uva.nl/id/eprint/402 |

## Actions (login required)

View Item |