A Theory of Program Size Formally Identical to Information Theory
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SIAM Journal on Computing
Journal of Computer and System Sciences
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Undecidability of the structure of the Solovay degrees of c.e. reals
Journal of Computer and System Sciences
On C-Degrees, H-Degrees and T-Degrees
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Non-cupping, measure and computably enumerable splittings
Mathematical Structures in Computer Science
Computability and Randomness
Kolmogorov complexity of initial segments of sequences and arithmetical definability
Theoretical Computer Science
Computably enumerable sets in the solovay and the strong weak truth table degrees
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Maximal Pairs of Computably Enumerable Sets in the Computably Lipschitz Degrees
Theory of Computing Systems
On the Gap Between Trivial and Nontrivial Initial Segment Prefix-Free Complexity
Theory of Computing Systems
Analogues of Chaitin's Omega in the computably enumerable sets
Information Processing Letters
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We show that there are Turing complete computably enumerable sets of arbitrarily low nontrivial initial segment prefix-free complexity. In particular, given any computably enumerable set A with nontrivial prefix-free initial segment complexity, there exists a Turing complete computably enumerable set B with complexity strictly less than the complexity of A. On the other hand it is known that sets with trivial initial segment prefix-free complexity are not Turing complete. Moreover we give a generalization of this result for any finite collection of computably enumerable sets A"i, i