Shannon Information and Kolmogorov Complexity
<|reference_start|>Shannon Information and Kolmogorov Complexity: We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and where they are fundamentally different. We discuss and relate the basic notions of both theories: Shannon entropy versus Kolmogorov complexity, the relation of both to universal coding, Shannon mutual information versus Kolmogorov (`algorithmic') mutual information, probabilistic sufficient statistic versus algorithmic sufficient statistic (related to lossy compression in the Shannon theory versus meaningful information in the Kolmogorov theory), and rate distortion theory versus Kolmogorov's structure function. Part of the material has appeared in print before, scattered through various publications, but this is the first comprehensive systematic comparison. The last mentioned relations are new.<|reference_end|>
@article{grunwald2004shannon,
    title={Shannon Information and Kolmogorov Complexity},
    author={Peter Grunwald (CWI) and Paul Vitanyi (CWI and University of
  Amsterdam)},
    journal={There are some errors in this paper draft; when in doubt see the
  textbook Li, Vitanyi, An Introduction to Kolmogorov Complexity and Its
  Applications, Springer, 1993, 1997, 2008, 2019},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0410002},
    primaryClass={cs.IT math.IT}
}