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On the other hand, Ψ has two rules that can change it, thus it is nonterminal. 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.
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 grammar describes which strings from an alphabet of a formal language are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language.
In terms of context-free grammar, a nonterminal is left-recursive if the leftmost symbol in one of its productions is itself (in the case of direct left recursion) or can be made itself by some sequence of substitutions (in the case of indirect left recursion).
Let us notate a formal grammar as = (,,,), with a set of nonterminal symbols, a set of terminal symbols, a set of production rules, and the start symbol.. A string () directly yields, or directly derives to, a string (), denoted as , if v can be obtained from u by an application of some production rule in P, that is, if = and =, where () is a production rule, and , is the unaffected left and ...
By deleting in this grammar each ε-rule, unless its left-hand side is the start symbol, the transformed grammar is obtained. [4]: 90 For example, in the following grammar, with start symbol S 0, S 0 → AbB | C B → AA | AC C → b | c A → a | ε. the nonterminal A, and hence also B, is nullable, while neither C nor S 0 is.
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
A right-regular grammar (also called right-linear grammar) is a formal grammar (N, Σ, P, S) in which all production rules in P are of one of the following forms: A → a; A → aB; A → ε; where A, B, S ∈ N are non-terminal symbols, a ∈ Σ is a terminal symbol, and ε denotes the empty string, i.e. the string of length 0. S is called the ...