Randomness, relativization and Turing degrees
@article{Nies2005RandomnessRA,
title={Randomness, relativization and Turing degrees},
author={A. Nies and F. Stephan and S. Terwijn},
journal={J. Symb. Log.},
year={2005},
volume={70},
pages={515-535}
}We compare various notions of algorithmic randomness. First we consider relativized randomness. A set is ?-random if it is Martin-L?f random relative to 0_1). We show that a set is 2-random if and only if there is a constant c such that infinitely many initial segments x of the set are c-incompressible: C(x) > |x| ? c. The 'only if direction was obtained independently by Joseph Miller. This characterization can be extended to the case of time-bounded C -complexity. Next we prove some results on… CONTINUE READING
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References
SHOWING 1-10 OF 50 REFERENCES
Recursively Enumerable Sets Modulo Iterated Jumps and Extensions of Arslanov's Completeness Criterion
- Mathematics, Computer Science
- J. Symb. Log.
- 1989
- 50