Let L be any formal language and it is given that L* is regular. Then select…
Let L be any formal language and it is given that L* is regular. Then select the correct statement about L.
Answer: C. L may or may not be regular — Explanation: L may or may not be regular. Case 1: L is non-regular. For example, let L = {a^p | p is prime}. This is non-regular. Then L* = {a*} - {ϵ, a},…
- A.
L must be regular
- B.
L must be non-regular
- C.
L may or may not be regular
- D.
L must be finite
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Correct answer: C
Explanation:
L may or may not be regular.
Case 1: L is non-regular. For example, let L = {a^p | p is prime}. This is non-regular. Then L* = {a*} - {ϵ, a}, which is regular.
Case 2: L is regular. For example, let L = {a}. This is regular (finite). Then L* = a* is also regular.
Thus, if L* is regular, L can be either regular or non-regular. Therefore, L may or may not be regular.