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Diskretn. Anal. Issled. Oper., 2013, Volume 20, Number 6, Pages 77–94 (Mi da754)  

This article is cited in 5 scientific papers (total in 5 papers)

On complexity measures for complexes of faces in the unit cube

I. P. Chukhrov

Institute for Computer Aided Design, RAS, 19/18 2nd Brestskaia St., 123056 Moscow, Russia

Abstract: We study the problem of proving that the complex of faces is minimal in the unit $n$-dimensional cube. We formulate sufficient conditions which enable us to prove that a complex of faces is minimal using the ordinal properties of the complexity measure functional and structural properties of Boolean functions. It makes it possible to expand the set of complexes of faces which are proven to be minimal with respect to complexity measures satisfying certain properties. We prove the strict inclusion for the following sets of complexes of faces: kernel, minimal for any complexity measure and minimal for any complexity measure, which is invariant under the replacement faces on isomorphic faces. Ill. 2, bibliogr. 10.

Keywords: face, complex of faces in the $n$-dimensional unit cube, Boolean function, complexity measure, minimal complex of faces.

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English version:
Journal of Applied and Industrial Mathematics, 2014, 8:1, 9–19

Bibliographic databases:

UDC: 519.714.7
Received: 09.11.2012

Citation: I. P. Chukhrov, “On complexity measures for complexes of faces in the unit cube”, Diskretn. Anal. Issled. Oper., 20:6 (2013), 77–94; J. Appl. Industr. Math., 8:1 (2014), 9–19

Citation in format AMSBIB
\Bibitem{Chu13}
\by I.~P.~Chukhrov
\paper On complexity measures for complexes of faces in the unit cube
\jour Diskretn. Anal. Issled. Oper.
\yr 2013
\vol 20
\issue 6
\pages 77--94
\mathnet{http://mi.mathnet.ru/da754}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3185265}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 1
\pages 9--19
\crossref{https://doi.org/10.1134/S1990478914010025}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84894369529}


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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, “Minimalnye kompleksy granei sluchainoi bulevoi funktsii”, Diskretn. analiz i issled. oper., 21:5 (2014), 76–94  mathnet  mathscinet
    2. I. P. Chukhrov, “On the problem of minimizing a single set of Boolean functions”, J. Appl. Industr. Math., 9:3 (2015), 335–350  mathnet  crossref  crossref  mathscinet  elib
    3. 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
    4. I. P. Chukhrov, “On the complexity of minimizing quasicyclic Boolean functions”, J. Appl. Industr. Math., 12:3 (2018), 426–441  mathnet  crossref  crossref  elib
    5. 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
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