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Prikl. Diskr. Mat. Suppl., 2017, Issue 10, Pages 149–151 (Mi pdma323)  

This article is cited in 2 scientific papers (total in 2 papers)

Mathematical Foundations of Informatics and Programming

An analogue of implicit mapping theorem to formal grammars

O. I. Egorushkin, I. V. Kolbasina, K. V. Safonov

M. F. Reshetnev Siberian State Aerospace University, Krasnoyarsk

Abstract: In the paper, some approaches to solving the systems of non-commutative polynomial equations in the form of formal power series (FPS) are developed. The approaches are based on the relation of such equations with the corresponding commutative equations. Every FPS is mapped to its commutative image – power series, which is obtained under the assumption that the symbols in it denote commutative variables with the values in the field of complex numbers. The consistency of the system of non-commutative polynomial equations, which is not directly connected with the consistency of its commutative image, is investigated. However, the analogue of the implicit mapping theorem to formal grammars (non-commutative systems) is obtained, namely if the condition of the implicit mapping theorem holds for the commutative image of the system, then not only this, but the initial non-commutative system of equations has a unique solution in the form of FPS.

Keywords: systems of polynomial equations, non-commutative variables, formal power series, commutative image, Jacobian.

DOI: https://doi.org/10.17223/2226308X/10/58

Full text: PDF file (544 kB)
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UDC: 519.682

Citation: O. I. Egorushkin, I. V. Kolbasina, K. V. Safonov, “An analogue of implicit mapping theorem to formal grammars”, Prikl. Diskr. Mat. Suppl., 2017, no. 10, 149–151

Citation in format AMSBIB
\Bibitem{EgoKolSaf17}
\by O.~I.~Egorushkin, I.~V.~Kolbasina, K.~V.~Safonov
\paper An analogue of implicit mapping theorem to formal grammars
\jour Prikl. Diskr. Mat. Suppl.
\yr 2017
\issue 10
\pages 149--151
\mathnet{http://mi.mathnet.ru/pdma323}
\crossref{https://doi.org/10.17223/2226308X/10/58}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Kishkan, K. V. Safonov, “Sintaksicheskii analiz monomov kontekstno-svobodnykh yazykov s uchetom poryadka primeneniya produktsii”, PDM. Prilozhenie, 2019, no. 12, 194–196  mathnet  crossref  elib
    2. I. V. Kolbasina, K. V. Safonov, “Uslovie razreshimosti proizvolnykh formalnykh grammatik”, PDM. Prilozhenie, 2019, no. 12, 196–198  mathnet  crossref  elib
  • Prikladnaya Diskretnaya Matematika. Supplement
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