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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.
A context-free grammar G is defined by the 4-tuple = (,,,), where [a] V is a finite set; each element is called a nonterminal character or a variable. Each variable represents a different type of phrase or clause in the sentence. Variables are also sometimes called syntactic categories.
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]
The grammar = (,,,) is effectively the semi-Thue system (,), rewriting strings in exactly the same way; the only difference is in that we distinguish specific nonterminal symbols, which must be rewritten in rewrite rules, and are only interested in rewritings from the designated start symbol to strings without nonterminal symbols.
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 ...
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.
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
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 ...
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