Syntax diagrams as a formalism for representation of syntactic relations of formal languages

TL;DR

This paper introduces syntax diagrams as a formalism for representing syntactic relations in formal languages, especially those with nonlinear text structures, using neighborhood grammars for correctness verification.

Contribution

It proposes a novel formalism of syntax diagrams combined with neighborhood grammars to describe and verify syntactic relations in complex, nonlinear formal languages.

Findings

Syntax diagrams effectively represent nonlinear syntactic structures.

Neighborhood grammars define correct syntax constructs.

The formalism allows systematic verification of syntax correctness.

Abstract

The new approach to representation of syntax of formal languages-- a formalism of syntax diagrams is offered. Syntax diagrams look a convenient language for the description of syntactic relations in the languages having nonlinear representation of texts, for example, for representation of syntax lows of the language of structural chemical formulas. The formalism of neighbourhood grammar is used to describe the set of correct syntax constructs. The neighbourhood the grammar consists of a set of families of "neighbourhoods"-- the diagrams defined for each symbol of the language's alphabet. The syntax diagram is correct if each symbol is included into this diagram together with some neighbourhood. In other words, correct diagrams are needed to be covered by elements of the neighbourhood grammar. Thus, the grammar of formal language can be represented as system of the covers defined for each correct syntax diagram.