Regular expressions provide a representation of Regular languages.

## Atomic

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 \(\{\epsilon\}\).

## Compound

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) \(R^*\)