LIPIcs.STACS.2009.1810.pdf
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Kolmogorov Complexity and Solovay Functions
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26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication Date: 2009-02-19
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Laurent Bienvenu and Rod Downey. Kolmogorov Complexity and Solovay Functions. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 147-158, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/LIPIcs.STACS.2009.1810
https://doi.org/10.4230/LIPIcs.STACS.2009.1810
Abstract
Solovay (1975) proved that there exists a computable upper bound~$f$ of the prefix-free Kolmogorov complexity function~$K$ such that $f(x)=K(x)$ for infinitely many~$x$. In this paper, we consider the class of computable functions~$f$ such that $K(x) \leq f(x)+O(1)$ for all~$x$ and $f(x) \leq K(x)+O(1)$ for infinitely many~$x$, which we call Solovay functions. We show that Solovay functions present interesting connections with randomness notions such as Martin-L\"of randomness and K-triviality.
Keywords
- Algorithmic randomness
- Kolmogorov complexity
- K-triviality
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