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# Chomsky normal form

A grammar is said to be of *Chomsky normal form* if every production
has either of the two forms

$A\to BC\qquad\mbox{ or }\qquad A\to a$ |

where $A,B,C$ are non-terminal symbols, and $a$ is a terminal symbol.

Grammars of this sort are context-free, hence they describe context-free languages. Moreover, given any context-free language not containing the empty word $\lambda$, there exists a Chomsky normal form grammar which describes it.

Related:

GreibachNormalForm, KurodaNormalForm

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## Mathematics Subject Classification

68Q42*no label found*68Q45

*no label found*

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