Math and science::Theory of Computation

Regular language operators

Let $$A$$ and $$B$$ be languages. We define the regular operations union, concatenation and star as follows:

Union
$$A \cup B = \{x \mid x \in A \lor x \in B\}$$  (i.e. as per standard axiom of union for sets)
Concatenation
$$A \circ B = \{ [...] \mid x \in A \land y \in B \}$$
Star
$$A^\star = \{ [...] \mid k \ge 0 \text{ and each } x_i \in A \}$$

The class of regular languages is [...]!