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The Tsallis entropy and the Shannon entropy of a universal probability | Kohtaro Tadaki
; | Date: |
1 May 2008 | Abstract: | We study the properties of Tsallis entropy and Shannon entropy from the point
of view of algorithmic randomness. In algorithmic information theory, there are
two equivalent ways to define the program-size complexity K(s) of a given
finite binary string s. In the standard way, K(s) is defined as the length of
the shortest input string for the universal self-delimiting Turing machine to
output s. In the other way, the so-called universal probability m is introduced
first, and then K(s) is defined as -log_2 m(s) without reference to the concept
of program-size. In this paper, we investigate the properties of the Shannon
entropy, the power sum, and the Tsallis entropy of a universal probability by
means of the notion of program-size complexity. We determine the convergence or
divergence of each of these three quantities, and evaluate its degree of
randomness if it converges. | Source: | arXiv, 0805.0154 | Services: | Forum | Review | PDF | Favorites |
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