On the number of infinite sequences with trivial initial segment complexity

被引：3

作者：

Barmpalias, George ^{[1
]}

Sterkenburg, T. F. ^{[2
]}

机构：

[1] Chinese Acad Sci, State Key Lab Comp Sci, Inst Software, Beijing 100190, Peoples R China

[2] Univ Amsterdam, Inst Log Language & Computat, NL-1090 GE Amsterdam, Netherlands

来源：

THEORETICAL COMPUTER SCIENCE | 2011年 / 412卷 / 52期

关键词：

Kolmogorov complexity; K-trivial sets; Arithmetical complexity; Trees; LOWNESS;

D O I：

10.1016/j.tcs.2011.09.020

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The sequences which have trivial prefix-free initial segment complexity are known as K-trivial sets, and form a cumulative hierarchy of length omega. We show that the problem of finding the number of K-trivial sets in the various levels of the hierarchy is Delta(0)(3). This answers a question of Downey/Miller/Yu (see Downey (2010) [7, Section 10.1.4]) which also appears in Nies (2009) [17, 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 a shorter initial segment complexity compared to the computable oracles. In both cases the classification Delta(0)(3) is sharp. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：7133 / 7146

页数：14