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MASS PROBLEMS AND INITIAL SEGMENT COMPLEXITY

Published online by Cambridge University Press:  17 April 2014

W. M. PHILLIP HUDELSON
W. M. PHILLIP HUDELSON*
Affiliation:
301 GRANT STREET, SUITE 2600, PITTSBURGH, PA 15219, USA E-mail: phil.hudelson@gmail.com
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Abstract

By the complexity of a finite sequence of 0’s and 1’s wemean the Kolmogorov complexity, that is the length of the shortest input to auniversal recursive function which returns the given sequence as output. Byinitial segment complexity of an infinite sequence of 0’s and1’s we mean the asymptotic behavior of the complexity of its finiteinitial segments. In this paper, we construct infinite sequences of0’s and 1’s with given recursive lower bounds on initialsegment complexity which do not compute any infinite sequences of 0’sand 1’s with a significantly larger recursive lower bound on initialsegment complexity. This improves several known results about randomnessextraction and separates many natural degrees in the lattice of Muchnikdegrees.

Keywords

Partial randomnessalgorithmic randomnessKolmogorov complexityMartin-Löf randomnesseffective Hausdorff dimension

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 1 , March 2014 , pp. 20 - 44
Copyright
Copyright © Association for Symbolic Logic 2014 

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