Geodesic
On application of multidimensional complex analysis in formal language and grammar theory
Prikladnaâ diskretnaâ matematika, no. 3 (2017), pp. 76-89

Voir la notice de l'article provenant de la source Math-Net.Ru

Systems of polynomial equations over a semiring (with respect to symbols with a non-commutative multiplication and a commutative addition) are investigated. These systems of equations are interpreted as the grammars of formal languages and are resolved with respect to the non-terminal symbols in the form of the formal power series (FPS) depending on the terminal symbols. The commutative image of the system of equations is determined under the assumption that the symbols are variables taking values from the field of complex numbers. The connections between solutions of the non-commutative symbolic system of equations and its commutative image are established, thus the methods for multidimensional complex analysis are involved in the theory of formal language grammars. A discrete analogue of implicit mapping theorem onto formal grammars is proved: a sufficient condition for the existence and the uniqueness of a solution of a non-commutative system of equations in the form of FPS is the inequality to zero of the Jacobian of the commutative image of this system. A new method for syntactic analysis of the monomials of a context-free language as a model of programming languages is also proposed. The method is based on the integral representation of the syntactic polynomial of a program. It is shown that the integral of a fixed multiplicity over a cycle allows finding the syntactic polynomial of a monomial (program) with the unlimited number of symbols, that gives a new approach to the problem of syntactic analysis.
Keywords: formal power series, commutative image, syntactic analysis, integral representation. 
@article{PDM_2017_3_a5,
     author = {O. I. Egorushkin and I. V. Kolbasina and K. V. Safonov},
     title = {On application of multidimensional complex analysis in formal language and grammar theory},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {76--89},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2017_3_a5/}
}
TY  - JOUR
AU  - O. I. Egorushkin
AU  - I. V. Kolbasina
AU  - K. V. Safonov
TI  - On application of multidimensional complex analysis in formal language and grammar theory
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2017
SP  - 76
EP  - 89
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2017_3_a5/
LA  - ru
ID  - PDM_2017_3_a5
ER  - 
%0 Journal Article
%A O. I. Egorushkin
%A I. V. Kolbasina
%A K. V. Safonov
%T On application of multidimensional complex analysis in formal language and grammar theory
%J Prikladnaâ diskretnaâ matematika
%D 2017
%P 76-89
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2017_3_a5/
%G ru
%F PDM_2017_3_a5
O. I. Egorushkin; I. V. Kolbasina; K. V. Safonov. On application of multidimensional complex analysis in formal language and grammar theory. Prikladnaâ diskretnaâ matematika, no. 3 (2017), pp. 76-89. http://geodesic.mathdoc.fr/item/PDM_2017_3_a5/