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Nonterminal symbols are blue and terminal symbols are red. In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form
A formal language defined or generated by a particular grammar is the set of strings that can be produced by the grammar and that consist only of terminal symbols. Diagram 1 illustrates a string that can be produced with this grammar. Diagram 1. The string Б Б Б Б was formed by the grammar defined by the given production rules. This grammar ...
A context-sensitive grammar is a noncontracting grammar in which all rules are of the form αAβ → αγβ, where A is a nonterminal, and γ is a nonempty string of nonterminal and/or terminal symbols. However, some authors use the term context-sensitive grammar to refer to noncontracting grammars in general. [1]
Some do not permit the second form of rule and cannot transform context-free grammars that can generate the empty word. For one such construction the size of the constructed grammar is O(n 4) in the general case and O(n 3) if no derivation of the original grammar consists of a single nonterminal symbol, where n is the size of the original ...
Formally, a TDPL grammar G is a quadruple consisting of the following components: A finite set N of nonterminal symbols. A finite set Σ of terminal symbols that is disjoint from N. A finite set P of production rules, where a rule has one of the following forms: A → ε, where A is a nonterminal and ε is the empty string.
A conjunctive grammar is defined by the 4-tuple = (,,,) where . V is a finite set; each element is called a nonterminal symbol or a variable.Each variable represents a different type of phrase or clause in the sentence.
The language { www : w ∈ {a,b} *} is generable by an indexed grammar, but not by a linear indexed grammar, while both { ww : w ∈ {a,b} *} and { a n b n c n : n ≥ 1 } are generable by a linear indexed grammar. If both the original and the modified production rules are admitted, the language class remains the indexed languages. [16]
An unrestricted grammar is a formal grammar = (,,,), where . is a finite set of nonterminal symbols,; is a finite set of terminal symbols with and disjoint, [note 1]; is a finite set of production rules of the form , where and are strings of symbols in and is not the empty string, and
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