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. © 2012 Springer-Verlag.
CITATION STYLE
Zimand, M. (2012). Symmetry of information: A closer look. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7160 LNCS, pp. 241–246). https://doi.org/10.1007/978-3-642-27654-5_18
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