EXAMPLE $2\mathrm{.}3$

Consider grammar G$3=(\{$S$\},\{$a$,$ b$\},$ R$,$ S$).$ The set of rules, R$,$ is

S $->$ aSb $|$ SS $|\backslash$epsi $.$

This grammar generates strings such as abab, aaabbb, and aababb. You can see more easily what this language is if you think of a as a left parenthesis $($ and b as a right parenthesis $).$ Viewed in this way, L$($G$3)$ is the language of all strings of properly nested parentheses. Observe that the right$-$hand side of a rule may be the empty string $\backslash$epsi $.$