Visualization 2001 Conference (Acm
Visualization 2001 Conference (Acm
An Introduction to Kolmogorov Complexity and Its Applications
An Introduction to Kolmogorov Complexity and Its Applications
Counting dependent and independent strings
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Symmetry of Information and Bounds on Nonuniform Randomness Extraction via Kolmogorov Extractors
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Extracting kolmogorov complexity with applications to dimension zero-one laws
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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Symmetry of information establishes a relation between the information that x has about y (denoted I(x : y)) and the information that y has about x (denoted I(y : x)). In classical information theory, the two are exactly equal, but in algorithmical information theory, there is a small excess quantity of information that differentiates the two terms, caused by the necessity of packaging information in a way that makes it accessible to algorithms. It was shown in [Zim11] that in the case of strings with simple complexity (that is the Kolmogorov complexity of their Kolmogorov complexity is small), the relevant information can be packed in a very economical way, which leads to a tighter relation between I(x : y) and I(y : x) than the one provided in the classical symmetry-of-information theorem of Kolmogorov and Levin. We give here a simpler proof of this result.