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

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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• http://mi.mathnet.ru/eng/fpm/v15/i3/p33

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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. 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
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