GATE CS 2019 Set 1 — Question 17
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Theory of Computation → Finite Automata & Regular Languages → Closure Properties (Regular)
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Question
If is a regular language over , which one of the following languages is NOT regular?
Correct answer
(B) \ww^R w ∈ L\
Solution
Regular languages are closed under concatenation, reversal, prefix, and suffix operations.
1.Option (A): . Since is regular, is regular. The concatenation of two regular languages is regular. Thus, this language is regular.
2.Option (C): Prefix. Regular languages are closed under the prefix operation. Thus, this language is regular.
3.Option (D): Suffix. Regular languages are closed under the suffix operation. Thus, this language is regular.
4.Option (B): . Even if , the language becomes , which is the standard example of a Context-Free Language (CFL) that is NOT regular. It requires a stack to match the reverse string with , which a finite automaton cannot do.
Therefore, option (B) is NOT necessarily regular.Continue learning with Success Tracker
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