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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 [...]!