[PDF] are regular languages closed under infinite union

Conclusion: Regular Language is not closed under Infinite Union (? ?).
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  • Is an infinite union of regular languages regular?

    Note 2: The union of infinitely many regular languages is not necessarily regular.
    For example while { akbk } is regular for any natural number k , { anbn n is a natural number } which is the union of all the languages { akbk } , is not regular as we shall see later.

  • Are regular languages closed under union?

    Regular languages are closed under union, concatenation, star, and complementation.

  • What are regular languages not closed under?

    Notice that regular languages are not closed under the subset/superset relation.
    For example, 0*1* is regular, but its subset {On1n : n >= 0} is not regular, but its subset {01, 0011, 000111} is regular again.

  • What are regular languages not closed under?

    True; all finite languages are regular languages and regular languages are closed under union.

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