In formal language theory, a **context-free grammar** (**CFG**) is a formal grammar in which every production rule is of the form

*V*→*w*

where *V* is a *single* nonterminal symbol, and *w* is a string of terminals and/or nonterminals (*w* can be empty).

The languages generated by context-free grammars are known as the context-free languages.

A formal grammar is considered "context free" when its production rules can be applied regardless of the context of a nonterminal.

Context-free grammars are important in linguistics for describing the structure of sentences and words in natural language, and in computer science for describing the structure of programming languages and other formal languages.

In linguistics, some authors use the term **phrase structure grammar** to refer to context-free grammars, whereby phrase structure grammars are distinct from dependency grammars. In computer science, a popular notation for context-free grammars is Backus–Naur Form, or *BNF*.

Read more about Context-free Grammar: Background, Formal Definitions, Normal Forms, Undecidable Problems, Extensions, Subclasses, Linguistic Applications

### Other articles related to "grammar":

**Context-free Grammar**- Linguistic Applications

... Chomsky initially hoped to overcome the limitations of

**context-free grammars**by adding transformation rules ... Much of generative

**grammar**has been devoted to finding ways of refining the descriptive mechanisms of phrase-structure

**grammar**and transformation rules such that exactly the kinds of things can be expressed ... transformations that introduce and then rewrite symbols in a

**context-free**fashion) ...

### Famous quotes containing the word grammar:

“The old saying of Buffon’s that style is the man himself is as near the truth as we can get—but then most men mistake *grammar* for style, as they mistake correct spelling for words or schooling for education.”

—Samuel Butler (1835–1902)