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In fact, the language defined by a grammar is precisely the set of terminal strings that can be so derived. Context-free grammars are those grammars in which the left-hand side of each production rule consists of only a single nonterminal symbol. This restriction is non-trivial; not all languages can be generated by context-free grammars.
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.
The representation of a grammar is a set of syntax diagrams. Each diagram defines a "nonterminal" stage in a process. There is a main diagram which defines the language in the following way: to belong to the language, a word must describe a path in the main diagram. Each diagram has an entry point and an end point.
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.
(This means that the X-bar theory indirectly assumes that speakers have in their Universal Grammar a rule that determines the canonical linear order for them, depending on their native language.) On the other hand, under the Minimalist Program, there is no such canonical fundamentals since the lexical array does not constitute an ordered set .
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 ...
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.
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]
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