Shannon Information and Kolmogorov Complexity

@misc{citeulike:682, abstract = {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.}, author = {Grunwald, Peter and Vitanyi, Paul }, citeulike-article-id = {682}, eprint = {cs.IT/0410002}, keywords = {communication, complexity, computational, computerscience, entropy, information, kolmogorov, shannon, theory}, month = {October}, posted-at = {2006-01-30 09:35:45}, priority = {2}, title = {Shannon Information and Kolmogorov Complexity}, url = {http://arxiv.org/abs/cs.IT/0410002}, year = {2004} }

TY - ELEC ID - citeulike:682 L3 - citeulike-article-id:682 TI - Shannon Information and Kolmogorov Complexity N2 - 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. KW - communication KW - complexity KW - computational KW - computerscience KW - entropy KW - information KW - kolmogorov KW - shannon KW - theory AU - Grunwald, Peter AU - Vitanyi, Paul PY - 2004/10/01/ UR - http://arxiv.org/abs/cs.IT/0410002 ER -