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Diskretn. Anal. Issled. Oper., 2013, Volume 20, Number 2, Pages 88–101 (Mi da728)  

On maximal and minimal elements in partially ordered sets of Boolean degrees

S. S. Marchenkov

Lomonosov Moscow State University, Moscow, Russia

Abstract: The weakest variant of algorithmic reducibility called Boolean reducibility is considered. For various closed classes $Q$, the partially ordered sets $\mathcal L_Q$ of Boolean degrees are analyzed. It is proved that for many closed classes $Q$ the corresponding sets $\mathcal L_Q$ have no maximal elements. Examples of sufficiently large classes $Q$ are given for which the sets $\mathcal L_Q$ contain uncountably many maximal elements. It is established that for closed classes $T_{01}$ and $S$M the corresponding sets of degrees have uncountably many minimal elements. Bibliogr. 8.

Keywords: Boolean reducibility, closed classes of Boolean functions.

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English version:
Journal of Applied and Industrial Mathematics, 2013, 7:4, 549–556

Bibliographic databases:

UDC: 519.71
Received: 29.05.2012

Citation: S. S. Marchenkov, “On maximal and minimal elements in partially ordered sets of Boolean degrees”, Diskretn. Anal. Issled. Oper., 20:2 (2013), 88–101; J. Appl. Industr. Math., 7:4 (2013), 549–556

Citation in format AMSBIB
\Bibitem{Mar13}
\by S.~S.~Marchenkov
\paper On maximal and minimal elements in partially ordered sets of Boolean degrees
\jour Diskretn. Anal. Issled. Oper.
\yr 2013
\vol 20
\issue 2
\pages 88--101
\mathnet{http://mi.mathnet.ru/da728}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3113403}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 4
\pages 549--556
\crossref{https://doi.org/10.1134/S1990478913040091}


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