Kolmogorov complexity of initial segments of sequences and arithmetical definability

DOI10.1016/J.TCS.2011.06.006zbMath1235.68087OpenAlexW2034673847MaRDI QIDQ719306

George Barmpalias, C. S. Vlek

Publication date: 10 October 2011

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.tcs.2011.06.006

zbMATH Keywords

arithmetical complexity\(K\)-degreesrelative randomnessprefix-free Kolmogorov complexity

Mathematics Subject Classification ID

Algorithmic information theory (Kolmogorov complexity, etc.) (68Q30)

Related Items (8)

Nullifying randomness and genericity using symmetric difference ⋮ Lower bounds on the redundancy in computations from random oracles via betting strategies with restricted wagers ⋮ Universal computably enumerable sets and initial segment prefix-free complexity ⋮ On the gap between trivial and nontrivial initial segment prefix-free complexity ⋮ ON REALS WITH -BOUNDED COMPLEXITY AND COMPRESSIVE POWER ⋮ On the number of infinite sequences with trivial initial segment complexity ⋮ On effectively closed sets of effective strong measure zero ⋮ Solovay functions and their applications in algorithmic randomness

Cites Work

• Oscillation in the initial segment complexity of random reals
• Elementary differences between the degrees of unsolvability and degrees of compressibility
• On the number of infinite sequences with trivial initial segment complexity
• Relative randomness and cardinality
• The \(K\)-degrees, low for \(K\) degrees, and weakly low for \(K\) sets
• The Kolmogorov complexity of random reals
• On the gap between trivial and nontrivial initial segment prefix-free complexity
• Lowness properties and randomness
• Lowness notions, measure and domination
• Chaitin's halting probability and the compression of strings using oracles
• Kolmogorov complexity and the Recursion Theorem
• Algorithmic Randomness and Complexity
• Time-Bounded Kolmogorov Complexity and Solovay Functions
• A minimal pair of 𝐾-degrees
• Randomness and Computability: Open Questions
• Randomness, lowness and degrees
• On initial segment complexity and degrees of randomness
• Kolmogorov Complexity and Solovay Functions
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