Kobayashi compressibility

@article{Barmpalias2017KobayashiC,
  title={Kobayashi compressibility},
  author={George Barmpalias and Rodney G. Downey},
  journal={Theor. Comput. Sci.},
  year={2017},
  volume={675},
  pages={89-100}
}
Aspects of Chaitin's Omega
TLDR
The purpose of this survey is to expose developments and tell a story about Omega, which outlines its multifaceted mathematical properties and roles in algorithmic randomness.
Compression of Data Streams Down to Their Information Content
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A new coding method is devised that uniformly codes every stream into an algorithmically random stream, providing a strong analogue of Shannon’s source coding theorem for the algorithmic information theory.

References

SHOWING 1-10 OF 42 REFERENCES
Compressibility of Infinite Binary Sequences
TLDR
This work proposes some definitions, based on Kobayashi's notion of compressibility, of the polynomial-time computable sequences, and compares them to both the standard resource-bounded Kolmogorov complexity of infinite strings, and the uniform complexity.
On Kurtz randomness
On Innnite Sequences (almost) as Easy As
TLDR
This work proposes some deeni-tions, based on Kobayashi's notion of compressibility, and compares them to the standard resource-bounded Kolmogorov complexity of innnite strings, and some non-trivial coincidences and disagreements are proved.
Chaitin Ω numbers and halting problems
TLDR
The relative computational power between the base-two expansion of Ω and the halting problem by imposing the restriction to finite size on both the problems is considered.
Optimal asymptotic bounds on the oracle use in computations from Chaitin's Omega
Randomness and halting probabilities
TLDR
It follows that for any optimal machine U and any sufficiently small real r, there is a set X ⊆ 2≤ω recursive in ∅′ ⊕ r, such that ΩU[X] = r.
Kolmogorov Complexity and Instance Complexity of Recursively Enumerable Sets
  • M. Kummer
  • Computer Science, Mathematics
    SIAM J. Comput.
  • 1996
TLDR
The main part of the paper is concerned with instance complexity, introduced by Ko, Orponen, Schoning, and Watanabe in 1986, as a measure of the complexity of individual instances of a decision problem, and it is shown that for every r.
Anti-Complex Sets and Reducibilities with Tiny Use
TLDR
This work shows the equivalence of anti-complexity and other lowness notions such as r.e. traceability or being weak truth-table reducible to a Schnorr trivial set, and investigates its range and the range of its uniform counterpart.
Algorithmic Randomness and Complexity
TLDR
This chapter discusses Randomness-Theoretic Weakness, Omega as an Operator, Complexity of C.E. Sets, and other Notions of Effective Randomness.
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