For a regular expression e, let L(e) be the language generated by e. If e is an expression that has no Kleene star ∗ occurring in it, which of the following is true about e in general?

(A) L(e) is empty.

(B) L(e) is finite. 

(C) Complement of L(e) is empty. 

(D) Both L(e) and its complement are infinite.

Responses

sumitverma's picture

L(e) is finite. This is proved by a simple induction on the structure of the regular expression, using the fact that L(a) is finite for each letter a, and that unions and concatenations of finite languages are also finite.

sumitverma's picture

For every set L, the Kleene plus L+ equals the concatenation of L with L*. So if it is given that If e is an expression that has no Kleene star ∗ occurring in it, we can not talk about L+ .

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