Geodesic
On a solving of algebraic equations systems associated with context-free languages
Prikladnaâ diskretnaâ matematika, no. 2 (2008), pp. 8-11.

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Systems of algebraic equations (polynomial and linear) which appear in context-free languages theory are considered. The solution of the system is a set of formal power series expressing one group of variables trough the other group of variables considered as parameters. It is impossible to directly use the classical elimination processes for a non-commutative ring. The conditions of solubility of a polynomial equations system as well as possibility to make lower the order of a linear equations system are given in the article. 
@article{PDM_2008_2_a1,
     author = {O. I. Yegorushkin and D. A. Kalugin-Balashov and K. V. Safonov},
     title = {On a solving of algebraic equations systems associated with context-free languages},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {8--11},
     publisher = {mathdoc},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2008_2_a1/}
}
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O. I. Yegorushkin; D. A. Kalugin-Balashov; K. V. Safonov. On a solving of algebraic equations systems associated with context-free languages. Prikladnaâ diskretnaâ matematika, no. 2 (2008), pp. 8-11. http://geodesic.mathdoc.fr/item/PDM_2008_2_a1/