ON THE NUMBER OF INFINITE SEQUENCES WITH TRIVIAL INITIAL SEGMENT COMPLEXITY
| Citations: | 1 - 1 self |
BibTeX
@MISC{Barmpalias_onthe,
author = {George Barmpalias and Tom Sterkenburg},
title = {ON THE NUMBER OF INFINITE SEQUENCES WITH TRIVIAL INITIAL SEGMENT COMPLEXITY},
year = {}
}
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Abstract
Abstract. The sequences which have trivial prefix-free initial segment complexity are known as K-trivial sets, and form a cumulative hierarchy of length ω. 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. 1.
Citations
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