GATE CS 2025 Set 1 — Question 44
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Theory of Computation → Finite Automata & Regular Languages → Pumping Lemma (Regular)
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Question
Consider the following two languages over the alphabet :Which ONE of the following statements is CORRECT?
Correct answer
(C) L₁ is not a regular language but L₂ is a regular language.
Solution
: Here with , so every string of starts with , ends with and has length at least 3. Conversely, any string with belongs to (take , ). Hencewhich is regular.: A string is in exactly when it has a non-empty prefix that is also a suffix, with (so that is non-empty). Intersect with the regular language and take with :
- must start with (the first letter of ) and be a proper suffix of . The only proper suffix of starting with is , so .
- is a prefix of only if .
- Non-overlap: .
- (A) wrong: is not regular.
- (B) wrong: it is the other way round.
- (C) correct.
- (D) wrong: is regular.
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