Set of all Languages

languages

Definition

Def

The set of all languages over an alphabet is the power set of the set of all strings:

$$\mathcal{P}({\Sigma }^{\ast })$$

$⟨\mathcal{P}({\Sigma }^{\ast }),\cup ,\cdot ,\{\},\{\epsilon \}⟩$ forms a non-commutative semiring.