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Rules are often written in the form head → body; e.g., the rule a → b specifies that a can be replaced by b. In the classic formalization of generative grammars first proposed by Noam Chomsky in the 1950s, [2] [3] a grammar G consists of the following components: A finite set N of nonterminal symbols.
Chomsky (1959) introduced the Chomsky hierarchy, in which context-sensitive grammars occur as "type 1" grammars; general noncontracting grammars do not occur. [2]Chomsky (1963) calls a noncontracting grammar a "type 1 grammar", and a context-sensitive grammar a "type 2 grammar", and by presenting a conversion from the former into the latter, proves the two weakly equivalent.
This grammar is not context-free due to rule 3 and it is ambiguous due to the multiple ways in which rule 2 can be used to generate sequences of s. However, the language it generates is simply the set of all nonempty strings consisting of a {\displaystyle a} s and/or b {\displaystyle b} s.
A noncontracting grammar is a grammar in which for any production rule, of the form u → v, the length of u is less than or equal to the length of v. Every context-sensitive grammar is noncontracting, while every noncontracting grammar can be converted into an equivalent context-sensitive grammar; the two classes are weakly equivalent. [12]
To remove it, for each rule B → X 1... X n, where X 1... X n is a string of nonterminals and terminals, add rule A → X 1... X n. unless this is a unit rule which has already been (or is being) removed. The skipping of nonterminal symbol B in the resulting grammar is possible due to B being a member of the unit closure of nonterminal symbol ...
An extended context-free grammar (or regular right part grammar) is one in which the right-hand side of the production rules is allowed to be a regular expression over the grammar's terminals and nonterminals. Extended context-free grammars describe exactly the context-free languages.
A grammar that uses phrase structure rules is a type of phrase structure grammar. Phrase structure rules as they are commonly employed operate according to the constituency relation, and a grammar that employs phrase structure rules is therefore a constituency grammar; as such, it stands in contrast to dependency grammars, which are based on ...
A → wB, where A and B are in N and w is in Σ *. Some authors call this type of grammar a right-regular grammar (or right-linear grammar) [1] and the type above a strictly right-regular grammar (or strictly right-linear grammar). [2] An extended left-regular grammar is one in which all rules obey one of A → w, where A is a non-terminal in N ...