Chomsky normal form

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

$$A\to BC\mathit{\hspace{1em}\hspace{1em}}\text{ or }\mathit{\hspace{1em}\hspace{1em}}A\to a$$

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-freelanguages. Moreover, given any context-free language not containing the empty word $\lambda$, there exists aChomsky normal form grammar which describes it.