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Some Questions on Polynomially Computable Representations for Generating Grammars and Backus–Naur Forms

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Abstract

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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Funding

The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics, SB RAS (project no. FWNF-2022-0011).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    A. V. Nechesov

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  1. A. V. Nechesov
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Correspondence to A. V. Nechesov.

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Nechesov, A.V. Some Questions on Polynomially Computable Representations for Generating Grammars and Backus–Naur Forms. Sib. Adv. Math. 32, 299–309 (2022). https://doi.org/10.1134/S1055134422040058

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  • DOI: https://doi.org/10.1134/S1055134422040058

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