Relations between varieties of Kolmogorov complexities
Abstract: "There are several sorts of Kolmogorov complexity, better to say several Kolmogorov complexities: decision complexity, simple complexity, prefix complexity, monotonic complexity, a priori complexity. The last three can and the first two cannot be used for defining randomness of an inf...
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1993
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| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS
93,29 |
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| Zusammenfassung: | Abstract: "There are several sorts of Kolmogorov complexity, better to say several Kolmogorov complexities: decision complexity, simple complexity, prefix complexity, monotonic complexity, a priori complexity. The last three can and the first two cannot be used for defining randomness of an infinite binary sequence. All those five versions of Kolmogorov complexity were considered, from a unified point of view, in a paper by the first author which appeared in O. Watanabe's book [5], and which is included as a supplement of this report, with the kind permission of Springer-Verlag. Upper and lower bounds for those complexities and also for their differences were announced in that paper without proofs. The purpose of this paper is to give proofs for those bounds In this paper, the word 'entropy' (not in a physical sense) is used instead of 'complexity'. This is a Moscow tradition suggested by A.N. Kolmogorov himself. By this tradition the term 'complexity' relates to any mode of description and 'entropy' is the complexity related to an optimal mode (i.e. to a mode that, roughly speaking, gives the shortest descriptions). |
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| Beschreibung: | 38 S. |