Regular expressions define formal languages as sets of strings over a finite alphabet. Let 
denote a selected alphabet. Then 
is a regular expression that denotes the empty
set and 
is a regular expression that denotes the set containing the empty string as its only
element.
If 
,
then 
is a regular expression that denotes the set whose only element is string 
. If 
and 
are regular expressions denoting sets 
and 
, then
1. 
is a regular expression denoting the set 
, where 
denotes the union.
2. 
is a regular expression denoting the set of all concatenations of 
and 
, where 
and 
.
3. 
is a regular expression denoting closure of 
, that is, the set of zero or more concatenations of strings
from 
The languages defined by regular expressions are regular languages, also called regular sets. A language is regular iff it is defined by a right linear grammar.
