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- K-trivial_set abstract "In mathematics, a set of natural numbers is called a K-trivial set if its initial segments viewed as binary strings are easy to describe: the prefix-free Kolmogorov complexity is as low as possible, close to that of a computable set. Solovay proved in 1975 that a set can be K-trivial without being computable.The Schnorr–Levin theorem says that random sets have a high initial segment complexity. Thus the K-trivials are far from random. This is why these sets are studied in the field of algorithmic randomness, which is a subfield of Computability theory and related to algorithmic information theory in computer science.At the same time, K-trivial sets are close to computable. For instance, they are all superlow, i.e. sets whose Turing jump is computable from the Halting problem, and form a Turing ideal, i.e. class of sets closed under Turing join and closed downward under Turing reduction.".
- K-trivial_set wikiPageID "41341441".
- K-trivial_set wikiPageRevisionID "598517580".
- K-trivial_set subject Category:Algorithmic_information_theory.
- K-trivial_set subject Category:Computability_theory.
- K-trivial_set comment "In mathematics, a set of natural numbers is called a K-trivial set if its initial segments viewed as binary strings are easy to describe: the prefix-free Kolmogorov complexity is as low as possible, close to that of a computable set. Solovay proved in 1975 that a set can be K-trivial without being computable.The Schnorr–Levin theorem says that random sets have a high initial segment complexity. Thus the K-trivials are far from random.".
- K-trivial_set label "K-trivial set".
- K-trivial_set label "K自明集合".
- K-trivial_set sameAs K自明集合.
- K-trivial_set sameAs m.0_x5t3s.
- K-trivial_set sameAs Q15958734.
- K-trivial_set sameAs Q15958734.
- K-trivial_set wasDerivedFrom K-trivial_set?oldid=598517580.
- K-trivial_set isPrimaryTopicOf K-trivial_set.