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 Prikl. Diskr. Mat. Suppl., 2019, Issue 12, Pages 196–198 (Mi pdma470)

Mathematical Foundations of Informatics and Programming

A solvability condition for arbitrary formal grammars

I. V. Kolbasina, K. V. Safonov

M. F. Reshetnev Siberian State University of Science and Technologies

Abstract: In the paper, approaches to solving the systems of non-commutative polynomial equations in the form of formal power series (FPS) based on the connection with the corresponding commutative equations are developed. Every FPS is mapped to its commutative image — power series, which is obtained under the assumption that the symbols denote commutative variables assigned as values in the field of complex numbers. The consistency of the system of noncommutative polynomial equations, which is not directly connected with the consistency of its commutative image, is investigated. However, the analogue of implicit mapping theorem to arbitrary formal grammars (non-commutative systems) is obtained, namely if the rank of Jacoby matrix for the commutative image of a system of equations is maximal, then the initial noncommutative 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/12/55

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UDC: 519.682

Citation: I. V. Kolbasina, K. V. Safonov, “A solvability condition for arbitrary formal grammars”, Prikl. Diskr. Mat. Suppl., 2019, no. 12, 196–198

Citation in format AMSBIB
\Bibitem{KolSaf19} \by I.~V.~Kolbasina, K.~V.~Safonov \paper A solvability condition for arbitrary formal grammars \jour Prikl. Diskr. Mat. Suppl. \yr 2019 \issue 12 \pages 196--198 \mathnet{http://mi.mathnet.ru/pdma470} \crossref{https://doi.org/10.17223/2226308X/12/55} \elib{https://elibrary.ru/item.asp?id=41153931}