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Diskretn. Anal. Issled. Oper., 2015, Volume 22, Number 3, Pages 75–97 (Mi da820)  

This article is cited in 2 scientific papers (total in 2 papers)

On the problem of minimizing a single set of Boolean functions

I. P. Chukhrov

Institute of Computer Aided Design RAS, 19/18 2-nd Brestskaya St., 123056 Moscow, Russia

Abstract: We study the set of Boolean functions that consist of a single connected component, have minimal complexes of faces which are not shortest and do not satisfy the sufficient condition for minimality based on the notion of an independent set of vertices. The independent minimization for the connected components and feasibility of sufficient conditions for the minimality can not be applied to minimizing of such functions. For this set of functions, we obtain lower bounds on the power and maximal number of complexes of faces which are minimal with respect to additive measures of linear and polynomial complexity. Ill. 1, bibliogr. 8.

Keywords: Boolean function, unit cube, face, complex of faces, additive complexity measure, shortest complex of faces, minimal complex of faces.

DOI: https://doi.org/10.17377/daio.2015.22.471

Full text: PDF file (495 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2015, 9:3, 335–350

Bibliographic databases:

UDC: 519.714.7
Received: 16.01.2015

Citation: I. P. Chukhrov, “On the problem of minimizing a single set of Boolean functions”, Diskretn. Anal. Issled. Oper., 22:3 (2015), 75–97; J. Appl. Industr. Math., 9:3 (2015), 335–350

Citation in format AMSBIB
\Bibitem{Chu15}
\by I.~P.~Chukhrov
\paper On the problem of minimizing a~single set of Boolean functions
\jour Diskretn. Anal. Issled. Oper.
\yr 2015
\vol 22
\issue 3
\pages 75--97
\mathnet{http://mi.mathnet.ru/da820}
\crossref{https://doi.org/10.17377/daio.2015.22.471}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3443299}
\elib{http://elibrary.ru/item.asp?id=23859893}
\transl
\jour J. Appl. Industr. Math.
\yr 2015
\vol 9
\issue 3
\pages 335--350
\crossref{https://doi.org/10.1134/S1990478915030059}


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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. I. P. Chukhrov, “Proof of covering minimality by generalizing the notion of independence”, J. Appl. Industr. Math., 11:2 (2017), 193–203  mathnet  crossref  crossref  elib
    2. I. P. Chukhrov, “On the minimization of Boolean functions for additive complexity measures”, J. Appl. Industr. Math., 13:3 (2019), 418–435  mathnet  crossref  crossref
  • Дискретный анализ и исследование операций
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