Analogues of Chaitin's Omega in the computably enumerable sets

作者:Barmpalias, G.*; Hoelzl, R.; Lewis, A. E. M.; Merkle, W.
来源:Information Processing Letters, 2013, 113(5-6): 171-178.
DOI:10.1016/j.ipl.2013.01.007

摘要

We show that there are computably enumerable (c.e.) sets with maximum initial segment Kolmogorov complexity amongst all c.e. sets (with respect to both the plain and the prefix-free version of Kolmogorov complexity). These c.e. sets belong to the weak truth table degree of the halting problem, but not every weak truth table complete c.e. set has maximum initial segment Kolmogorov complexity. Moreover, every c.e. set with maximum initial segment prefix-free complexity is the disjoint union of two c.e. sets with the same property; and is also the disjoint union of two c.e. sets of lesser initial segment complexity.

  • 出版日期2013-3
  • 单位中国科学院; 计算机科学国家重点实验室