Set of all Languages

languages

Definition

Set of all Languages

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

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

The structure $⟨\mathcal{P}({\Sigma }^{\ast }),\cdot ,\{\epsilon \}⟩$ forms a monoid.

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