the set theoretic Boolean operations: union K ∪ L, intersection K ∩ L, and complement L, hence also relative complement K - L.[13] the regular operations: K ∪ L, concatenation K ∘ L, and Kleene star L*.[14] 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 K / L 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.[citation needed] the reverse (or mirror image) LR.[15] Given a nondeterministic finite automaton to recognize L, an automaton for LR can be obtained by reversing all transitions and interchanging starting and finishing states.