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Fundam. Prikl. Mat., 2009, Volume 15, Issue 3, Pages 33–47 (Mi fpm1227)  

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

On the classification of bases in $P_k$ according to the decidability of the completeness problem for automata

D. N. Babin

M. V. Lomonosov Moscow State University

Abstract: The completeness problem for bases of the form $\Phi\cup\nu$, where $\Phi\subseteq P_k$ and $\nu$ is a finite system of automaton functions, is considered. Previously, the problem for $k=2$ was solved by the author; it was also shown that there is an algorithm for determining the completeness of the system $\Phi\cup\nu$ when $[\Phi]=P_k$. The article is concerned with the case where $[\Phi]$ is the maximal (precomplete) class in $P_k$. The problem of completeness for systems $\Phi\cup\nu$ is shown to be undecidable if $\Phi$ is embedded in a Slupecki class and algorithmically decidable if $\Phi$ contains the preserving class of all constants. Thus, the bases in $P_k$, $k\ge3$, can be classified according to their ability to guarantee the decidability of the completeness problem for automaton functions.

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English version:
Journal of Mathematical Sciences (New York), 2010, 168:1, 21–31

Bibliographic databases:

UDC: 519.95

Citation: D. N. Babin, “On the classification of bases in $P_k$ according to the decidability of the completeness problem for automata”, Fundam. Prikl. Mat., 15:3 (2009), 33–47; J. Math. Sci., 168:1 (2010), 21–31

Citation in format AMSBIB
\Bibitem{Bab09}
\by D.~N.~Babin
\paper On the classification of bases in $P_k$ according to the decidability of the completeness problem for automata
\jour Fundam. Prikl. Mat.
\yr 2009
\vol 15
\issue 3
\pages 33--47
\mathnet{http://mi.mathnet.ru/fpm1227}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2744971}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 168
\issue 1
\pages 21--31
\crossref{https://doi.org/10.1007/s10958-010-9972-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77954033138}


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    This publication is cited in the following articles:
    1. D. N. Babin, “Solvability of the problem of completeness of automaton basis depending on its boolean part”, Moscow University Mathematics Bulletin, 74:1 (2019), 32–34  mathnet  crossref  isi
  • Фундаментальная и прикладная математика
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