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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