Regular Language - Closure Properties

Closure Properties

The regular languages are closed under the various operations, that is, if the languages K and L are regular, so is the result of the following operations:

• the set theoretic Boolean operations: union, intersection, and complement . From this also relative complement follows.
• the regular operations: union, concatenation, and Kleene star .
• the trio operations: string homomorphism, inverse string homomorphism, and intersection with regular languages. As a consequence they are closed under arbitrary finite state transductions, like quotient with a regular language. Even more, regular languages are closed under quotients with arbitrary languages: If L is regular then L/K is regular for any K.
• the reverse (or mirror image) .