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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
