Every sequence is reducible to a random one
نویسندگان
چکیده
منابع مشابه
Every Sequence Is Reducible to a Random One
Charles Bennett asked whether every infinite binary sequence can be obtained from an "incompressible" one by a Turing machine, He proved that this is the case for arithmetical sequences. The question has some philosophical interest because it permits us to view even very pathological sequences as the result of the combination of two relatively wellunderstood processes: the completely chaotic ou...
متن کاملEvery sequence is compressible to a random one
Kučera and Gaćs independently showed that every infinite sequence is Turing reducible to a Martin-Löf random sequence. We extend this result to show that every infinite sequence S is Turing reducible to a Martin-Löf random sequence R such that the asymptotic number of bits of R needed to compute n bits of S, divided by n, is precisely the constructive dimension of S. We show that this is the op...
متن کاملEvery Sequence Is Decompressible from a Random One
Kučera and Gács independently showed that every infinite sequence is Turing reducible to a Martin-Löf random sequence. This result is extended by showing that every infinite sequence S is Turing reducible to a Martin-Löf random sequence R such that the asymptotic number of bits of R needed to compute n bits of S, divided by n, is precisely the constructive dimension of S. It is shown that this ...
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Kučera and Ga´cs independently showed that every infinite sequence is Turing reducible to a Martin-Löf random sequence. We extend this result to show that every infinite sequence S is Turing reducible to a Martin-Löf random sequence R such that the asymptotic number of bits of R needed to compute n bits of S, divided by n, is precisely the constructive dimension of S. We show that this is the o...
متن کاملEvery 2-random real is Kolmogorov random
We study reals with infinitely many incompressible prefixes. Call A ∈ 2 Kolmogorov random if (∃∞n) C(A n) > n − O(1), where C denotes plain Kolmogorov complexity. This property was suggested by Loveland and studied by Martin-Löf, Schnorr and Solovay. We prove that 2-random reals are Kolmogorov random.1 Together with the converse—proved by Nies, Stephan and Terwijn [11]—this provides a natural c...
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ژورنال
عنوان ژورنال: Information and Control
سال: 1986
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(86)80004-3