Regular expressions provide a representation of Regular languages.
The empty language, \(\emptyset\), is a regular expression that captures the empty language. Any symbol \(a\) in \(\Sigma\) is a regular expression for the language \(\{a\}\). Empty string, \(\epsilon\), is a regular expression representing the language \(\{\epsilon\}\).
Given two regular expressions \(R_1\) and \(R_2\) compound expressions may be formed through: Concatenation \(R_1 \circ R_2\) Alternation (union) \(R_1 \cup R_2\) Kleene star (repetition) \(R^*\)