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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 5, Pages 935–940 (Mi zvmmf660)  

This article is cited in 6 scientific papers (total in 6 papers)

On the number of irreducible coverings of an integer matrix

E. V. Dyukova

Dorodnicyn Computing Center Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: The metric (quantitative) properties of the set of coverings of an integer matrix are examined. an asymptotic estimate for the logarithm of the typical number of irredundant $\sigma$-coverings is obtained in the case when the number of rows in the matrix is not smaller than the number of its columns. as a consequence, a similar estimate is derived for the number of maximal conjunctions of a boolean function of $n$ variables with the number of zeros no less than $n$.

Key words: discrete recognition procedures, irredundant covering of an integer matrix, metric properties of a set of coverings, metric properties of disjunctive normal forms.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:5, 903–908

Bibliographic databases:
UDC: 519.6:519.712.63
Received: 26.11.2004

Citation: E. V. Dyukova, “On the number of irreducible coverings of an integer matrix”, Zh. Vychisl. Mat. Mat. Fiz., 45:5 (2005), 935–940; Comput. Math. Math. Phys., 45:5 (2005), 903–908

Citation in format AMSBIB
\Bibitem{Dyu05}
\by E.~V.~Dyukova
\paper On the number of irreducible coverings of an integer matrix
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 5
\pages 935--940
\mathnet{http://mi.mathnet.ru/zvmmf660}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2190083}
\zmath{https://zbmath.org/?q=an:1090.15014}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 5
\pages 903--908


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. A. Dem'yanov, E. V. Dyukova, “On the construction of irredundant coverings of an integer matrix”, Comput. Math. Math. Phys., 47:3 (2007), 518–526  mathnet  crossref  mathscinet  zmath
    2. Djukova E.V., “Construction of irredundant coverings of a Boolean matrix”, Dokl. Math., 75:1 (2007), 9–11  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Djukova E.V., Sotnezov R.M., “On the complexity of discrete generation problems”, Dokl. Math., 82:3 (2010), 847–849  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. E. V. Djukova, R. M. Sotnezov, “Asymptotic estimates for the number of solutions of the dualization problem and its generalizations”, Comput. Math. Math. Phys., 51:8 (2011), 1431–1440  mathnet  crossref  mathscinet  isi
    5. Rojas A., Cumplido R., Ariel Carrasco-Ochoa J., Feregrino C., Francisco Martinez-Trinidad J., “Hardware-software platform for computing irreducible testors”, Expert Systems with Applications, 39:2 (2012), 2203–2210  crossref  mathscinet  isi  elib  scopus
    6. E. V. Dyukova, R. M. Sotnezov, “On the complexity of the dualization problem”, Comput. Math. Math. Phys., 52:10 (2012), 1472–1481  mathnet  crossref  mathscinet  zmath
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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