PP-2010-23: On the number of infinite sequences with trivial initial segment complexity

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

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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

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