Given the following two languages: L₁ = { u w wᴿ v | u, v, w ∈ {a, b}⁺ } L₂ =…
2016
Given the following two languages:
L₁ = { u w wᴿ v | u, v, w ∈ {a, b}⁺ }
L₂ = { u w wᴿ v | u, v, w ∈ {a, b}⁺, |u| > |v| }
Which of the following is correct?
- A.
L₁ is regular language and L₂ is not regular language
- B.
L₁ is not regular language and L₂ is regular language
- C.
Both L₁ and L₂ are regular languages
- D.
Both L₁ and L₂ are not regular languages
Attempted by 20 students.
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Correct answer: A
L₁ is regular because any string in w wᴿ must contain a double letter ('aa' or 'bb'), allowing recognition by finite automata. L₂ requires comparing lengths of u and v, which demands memory beyond finite state capabilities, making it non-regular.
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