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Kolmogorov Complexity & Information Theory
Grunwald, Peter D. and Vitanyi, Paul M.B.

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Kolmogorov Complexity & Information Theory

Riassunto

Argomenti: [Informatica.AlgoritmieStrutturedati, Lang:en]

Editore: Kluwer Academic Publishers

Riassunto:

Journal of Logic, Language and Information 12: 497–529, 2003.
© 2003 Kluwer Academic Publishers.

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, Kolmogorov complexity,
Shannon mutual information and Kolmogorov (“algorithmic”) mutual information. We explain  how universal coding may be viewed as a middle ground between the two theories. We consider  Shannon’s rate distortion theory, which quantifies useful (in a certain sense) information. We use  the communication of information as our guiding motif, and we explain how it relates to sequential  question-answer sessions.
Key words: Algorithmic information theory, data compression, Kolmogorov complexity, mutual  information, prefix codes, rate distortion theory, Shannon information theory, universal codes.