RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 8, Pages 1531–1540 (Mi zvmmf9532)  

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

Asymptotic estimates for the number of solutions of the dualization problem and its generalizations

E. V. Djukovaa, R. M. Sotnezovb

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia
b Moscow State University, Moscow, 119992 Russia

Abstract: Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number $m$ of rows is no less than the number $n$ of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of $n$ variables defined by a conjunctive normal form of $m$ clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). Results obtained previously in this area are overviewed.

Key words: complexity of enumeration problems, dualization problem, maximal conjunction, irreducible covering of a Boolean matrix, irredundant covering of an integer matrix, complexity of search for irredundant coverings, metric properties of the set of coverings, metric properties of disjunctive normal forms, asymptotically optimal algorithm.

Full text: PDF file (709 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2011, 51:8, 1431–1440

Bibliographic databases:

UDC: 519.712
Received: 13.07.2010
Revised: 18.01.2011

Citation: E. V. Djukova, R. M. Sotnezov, “Asymptotic estimates for the number of solutions of the dualization problem and its generalizations”, Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011), 1531–1540; Comput. Math. Math. Phys., 51:8 (2011), 1431–1440

Citation in format AMSBIB
\Bibitem{DyuSot11}
\by E.~V.~Djukova, R.~M.~Sotnezov
\paper Asymptotic estimates for the number of solutions of the dualization problem and its generalizations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2011
\vol 51
\issue 8
\pages 1531--1540
\mathnet{http://mi.mathnet.ru/zvmmf9532}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2906725}
\transl
\jour Comput. Math. Math. Phys.
\yr 2011
\vol 51
\issue 8
\pages 1431--1440
\crossref{https://doi.org/10.1134/S0965542511080069}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000293977100015}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051779568}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf9532
  • http://mi.mathnet.ru/eng/zvmmf/v51/i8/p1531

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. 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
    Number of views:
    This page:192
    Full text:55
    References:25
    First page:8

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020