Geodesic
Some questions on polynomially computable representations for generating grammars and Backus-Naur forms
Matematičeskie trudy, Tome 25 (2022) no. 1, pp. 134-151

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In the present article, we consider the question on modeling Backus-Naur forms (BNF-systems) and generating grammars in GNF-systems. GNF-systems serve as the base for construction of monotone operators whose least fixed points are polynomially computable. We obtain our results by construction of GNF-systems and application of a generalized polynomial analog of Gandy's fixed point theorem. This allows us to answer some questions on existence of a polynomially computable representation for the set of derivations in generating grammars. Moreover, we show that, for each GNF-system modeling a BNF-system and every nonterminal symbol in the BNF-system, the set of preimages in the GNF-system of representations of this symbol is polynomially computable. This result allows us to encode all definable constructions of the BNF-system, including the syntax of programs in high-level programming languages, so that they become recognizable in polynomial time. 
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     author = {A. V. Nechesov},
     title = {Some questions on polynomially computable representations for generating grammars and {Backus-Naur} forms},
     journal = {Matemati\v{c}eskie trudy},
     pages = {134--151},
     publisher = {mathdoc},
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     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2022_25_1_a5/}
}
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A. V. Nechesov. Some questions on polynomially computable representations for generating grammars and Backus-Naur forms. Matematičeskie trudy, Tome 25 (2022) no. 1, pp. 134-151. http://geodesic.mathdoc.fr/item/MT_2022_25_1_a5/