Entropy Measures vs. Algorithmic Information

• Type: Article in International Conference Proceedings Book
• Date: 2010

Authors

teixeira, a (Author) Other; souto, a (Author) Other; matos, a (Author) FCUP; antunes, l (Author) FCUP

Conference proceedings International

Title: IEEE International Symposium on Information Theory (ISIT 2010), Austin TX, June 2010

Pages: 1413-1417

IEEE International Symposium on Information Theory (ISIT 2010), Austin TX, June 2010

Austin TX, JUL 13-13, 2010

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ISI Web of Knowledge - 0 Citations

Scopus - 1 Citation

Other information

Authenticus ID: P-003-DDF

DOI: 10.1109/isit.2010.5513643

Abstract (EN): Algorithmic entropy and Shannon entropy are two conceptually different information measures, as the former is based on size of programs and the later in probability distributions. However, it is known that, for any recursive probability distribution, the expected value of algorithmic entropy equals its Shannon entropy, up to a constant that depends only on the distribution. We study if a similar relationship holds for Renyi and Tsallis entropies of order a, showing that it only holds for Renyi and Tsallis entropies of order 1 (i.e., for Shannon entropy). Regarding a time bounded analogue relationship, we show that, for distributions such that the cumulative probability distribution is computable in time t(n), the expected value of time-bounded algorithmic entropy (where the alloted time is nt(n) log(nt(n))) is in the same range as the unbounded version. So, for these distributions, Shannon entropy captures the notion of computationally accessible information. We prove that, for universal time-bounded distribution m(t)(x), Tsallis and Renyi entropies converge if and only if a is greater than 1.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 5