Some lowness properties and computational complexity sequences
نویسندگان
چکیده
منابع مشابه
Computational Randomness and Lowness
We prove that there are uncountably many sets that are low for the class of Schnorr random reals. We give a purely recursion theoretic characterization of these sets and show that they all have Turing degree incomparable to 0 0. This contrasts with a result of Ku cera and Terwijn 5] on sets that are low for the class of Martin-LL of random reals. The Cantor space 2 ! is the set of innnite binar...
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15 صفحه اولLowness properties and randomness
The set A is low for (Martin-Löf) randomness if each random set is already random relative to A. A is K-trivial if the prefix complexity K of each initial segment of A is minimal, namely ∀n K(A!n)"K(n) + O(1). We show that these classes coincide. This answers a question of Ambos-Spies and Kučera in: P. Cholak, S. Lempp, M. Lerman, R. Shore, (Eds.), Computability Theory and Its Applications: Cur...
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Consider a randomness notion C. A uniform test in the sense of C is a total computable procedure that each oracle X produces a test relative to X in the sense of C. We say that a binary sequence Y is C-random uniformly relative to X if Y passes all uniform C tests relative to X. Suppose now we have a pair of randomness notions C and D where C ⊆ D, for instance Martin-Löf randomness and Schnorr ...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1978
ISSN: 0304-3975
DOI: 10.1016/0304-3975(78)90007-5