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# Regular expressions

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) $$R^*$$