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 sets defined by regular expressions are called regular sets, and a set is regular iff it is defined by a right linear grammar.