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Diskretn. Anal. Issled. Oper., 2012, Volume 19, Number 4, Pages 86–98 (Mi da700)  

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

On solutions to systems of automata-type functional equations

S. S. Marchenkov

Lomonosov Moscow State University, Moscow, Russia

Abstract: The automata-type functional equations are considered. These equations include subject variables for natural numbers and one-placed functional variables for infinite binary sequences. An algorithm is defined which solves the satisfiability problem for finite systems of functional equations containing only functions $1$ and $t+1$. The linear homogeneous structures are used to establish the lower bound for time complexity of similar deciding algorithms. It is proved that the satisfiability problem is algorithmically undecidable for the systems of functional equations which contain yet the functions $2t,3t$, and $5t$. Tab. 1, bibliogr. 10.

Keywords: automata-type functional equation, satisfiability problem.

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Bibliographic databases:
UDC: 519.7
Received: 04.10.2011

Citation: S. S. Marchenkov, “On solutions to systems of automata-type functional equations”, Diskretn. Anal. Issled. Oper., 19:4 (2012), 86–98

Citation in format AMSBIB
\Bibitem{Mar12}
\by S.~S.~Marchenkov
\paper On solutions to systems of automata-type functional equations
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 4
\pages 86--98
\mathnet{http://mi.mathnet.ru/da700}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3013546}


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    This publication is cited in the following articles:
    1. S. S. Marchenkov, “Definability in the language of functional equations of a countable-valued logic”, Discrete Math. Appl., 23:5-6 (2013), 451–462  mathnet  crossref  crossref  mathscinet  elib
  • Дискретный анализ и исследование операций
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