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Diskretn. Anal. Issled. Oper., 2012, Volume 19, Number 6, Pages 72–98 (Mi da713)  

This article is cited in 3 scientific papers (total in 3 papers)

Decomposition of underdetermined data

L. A. Sholomov

Institute of System Analysis RAS, Moscow, Russia

Abstract: For any underdetermined source in general form, we consider its decomposition as product of sources generating symbols 0, 1, and the indefinite symbol $*$. Also, we learn best approximate (in a prescribed sense) decomposition if correct decomposition is impossible. It is proved that the best approximate decomposition always exists and is unique up to some equivalence (for the decomposable source, it coincides with its decomposition). A polynomial algorithm to construct the approximate decomposition is proposed. Several problems related to simplifications and equivalent transformations of decompositions are studied. For them, some polynomial algorithms are proposed. Tabl. 4, bibliogr. 8.

Keywords: underdetermined source, information equivalence, decomposition, lower approximation, polynomial algorithm.

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English version:
Journal of Applied and Industrial Mathematics, 2013, 7:1, 100–116

Bibliographic databases:

UDC: 519.728
Received: 16.01.2012
Revised: 09.04.2012

Citation: L. A. Sholomov, “Decomposition of underdetermined data”, Diskretn. Anal. Issled. Oper., 19:6 (2012), 72–98; J. Appl. Industr. Math., 7:1 (2013), 100–116

Citation in format AMSBIB
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\by L.~A.~Sholomov
\paper Decomposition of underdetermined data
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 6
\pages 72--98
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3076915}
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\jour J. Appl. Industr. Math.
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\vol 7
\issue 1
\pages 100--116
\crossref{https://doi.org/10.1134/S1990478913010109}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. A. Sholomov, “O ponyatii ravnosilnosti nedoopredelennykh alfavitov”, PDM, 2014, no. 3(25), 40–57  mathnet
    2. Sholomov L.A., “on the Reducibility of Alphabets For Problems of Underdetermined Data Coding”, Dokl. Math., 91:1 (2015), 117–120  crossref  mathscinet  zmath  isi  elib  scopus
    3. L. A. Sholomov, “Ob odnom invariante v zadache razlozheniya nedoopredelennykh dannykh”, PDM, 2018, no. 39, 13–32  mathnet  crossref
  • Дискретный анализ и исследование операций
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