Computability in Europe 2006
Logical Approaches to Computational Barriers

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Regular Talk:
Every sequence is decompressible from a random one

Speaker: David Doty
Author(s): David Doty
Presentation: esdro-present-1.pdf
Slot: Tue, 11:30-11:50, Faraday A (col. 1)


Kučera and Gács 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 optimal ratio of query bits to computed bits achievable with Turing reductions. As an application of this result, we give a new characterization of constructive dimension in terms of Turing reduction compression ratios.

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