Regular Language

These are Languages that can be created from a Regex.

Formal Definition

$L=\mathcal{L}(R)$ for a given regex $R$ Where $\mathcal{L}(\cdot )$ is the Language of Regex

Language Properties

• $\mathcal{L}(\varnothing )=\varnothing$
• $\mathcal{L}(ϵ)=\{ϵ\}$
• $\mathcal{L}(c)=\{c\}$, $\forall c\in \Sigma$
• $\mathcal{L}((S+T))=\mathcal{L}(S)\cup \mathcal{L}(T)$
• $\mathcal{L}((ST))=\mathcal{L}(S)\mathcal{L}(T)$
• $\mathcal{L}(S^{\ast })=\mathcal{L}(S{)}^{\ast }$

Concepts

• Regex
• Closure of Regular Expressions