Abstract
Abstract
By the complexity of a finite sequence of 0’s and 1’s we
mean the Kolmogorov complexity, that is the length of the shortest input to a
universal recursive function which returns the given sequence as output. By
initial segment complexity of an infinite sequence of 0’s and
1’s we mean the asymptotic behavior of the complexity of its finite
initial segments. In this paper, we construct infinite sequences of
0’s and 1’s with given recursive lower bounds on initial
segment complexity which do not compute any infinite sequences of 0’s
and 1’s with a significantly larger recursive lower bound on initial
segment complexity. This improves several known results about randomness
extraction and separates many natural degrees in the lattice of Muchnik
degrees.
Publisher
Cambridge University Press (CUP)
Cited by
2 articles.
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