GATE CS 2022 Set 1 — Question 47
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Theory of Computation → Context-Free Languages
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Question
Consider the following languages:Note that is the reversal of the string . Which of the following is/are TRUE?
Correct answer
(A) L₁ and L₂ are regular.; (B) L₁ and L₂ are context-free.; (C) L₁ is regular and L₂ is context-free.
Solution
For : Since can be any string, we can choose , which gives . Even if is implied, . In either case, is regular.For : must be non-empty, so it starts with or . If starts with , ends with . Since , there is at least one character in between. Thus, any string starting and ending with with length is in (choose ). Similarly for . Thus , which is regular.Since both are regular, they are also context-free. Therefore, statements (A), (B), and (C) are all true.
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