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Prikladnaya Diskretnaya Matematika, 2014, Number 3(25), Pages 40–57 (Mi pdm471)  

This article is cited in 1 scientific paper (total in 1 paper)

Theoretical Foundations of Applied Discrete Mathematics

On the concept of underdetermined alphabets of equal strength

L. A. Sholomov

Institute of Systems Analysis, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (671 kB) Citations (1)
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Abstract: For underdetermined alphabets, the following two concepts are defined: a) one alphabet is stronger than another, and b) two alphabets have equal strength. To define concepts (a) and (b), several approaches are used. The functional approach is based on expressibility of one alphabet via another; three other approaches – combinatorial, probabilistic, and algorithmic – are terminologically connected with the Kolmogorov's approaches to the notion of the amount of information. It is proved that all these approaches to the comparison of alphabets are equivalent. In case (b), a solution of the optimal compression problem for one of the alphabets, in fact, solves the same problem for the other. It is shown that the concepts (a) and (b) allow polynomial time verification.
Keywords: underdetermined alphabet, alphabets of equal strength, entropy of underdetermined data, Kolmogorov complexity.
Document Type: Article
UDC: 621.391+519.728
Language: Russian
Citation: L. A. Sholomov, “On the concept of underdetermined alphabets of equal strength”, Prikl. Diskr. Mat., 2014, no. 3(25), 40–57
Citation in format AMSBIB
\Bibitem{Sho14}
\by L.~A.~Sholomov
\paper On the concept of underdetermined alphabets of equal strength
\jour Prikl. Diskr. Mat.
\yr 2014
\issue 3(25)
\pages 40--57
\mathnet{http://mi.mathnet.ru/pdm471}
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  • https://www.mathnet.ru/eng/pdm/y2014/i3/p40
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Прикладная дискретная математика
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