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

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. 1. The work’s motivation The idea of representation of syntax relations of a formal language by means of the definition of families of language symbols’ neighbourhoods belongs to Soviet mathematician J. Shreider ([4]). The neighbourhood of a symbol here is understood as any chain of symbols containing this symbol. The chain is in the source language if, and only if each symbol belongs to this chain together with some it’s neighbourhood. Such the system of neighbourhoods has been named by Shreider as a neighbourhood grammar. Let consider a concrete example. Let L be a formal language with the alphabet A = {a, b} and chains of language L are the sequences of alternating symbols a and b, where first and last symbols must be a. In other words, chains of language L are chains of a kind aba, ababa, abababa, etc. Let define the neighbourhood grammar for this language by enumerating a finite system of neighbourhoods for each symbol of the alphabet A. Let consider the symbol a and places in the language’s chains where it is occurred. This symbol necessarily appears in the beginning and the end of any chain of formal language L. To accent this fact, enter an additional pseudo-symbol # which will signal about the beginning and the end of a chain. Thus, there are two neighbourhoods of a symbol a: a neighbourhood #ab and a neighbourhood ba#. Except for the above-stated cases, the symbol