GATE CS 2015 Set 2 — Question 46
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Theory of Computation → Finite Automata & Regular Languages → Closure Properties (Regular)
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Question
Which of the following languages is/are regular?
Correct answer
(A) L₁ and L₃ only
Solution
1.Analyze : .
Since , can be any non-empty string. Consider any string with length . If the first symbol of is the same as the last symbol of , we can let be that symbol (length 1), and be the substring in between. Since , the middle part has length , so . Thus, consists of all strings of length that start and end with the same symbol. This can be represented by the regular expression: . Hence, is Regular.2.Analyze : .
This is a classic Context-Free Language (CFL) that is not Regular. Its complement (intersected with ) is , which requires a stack to check equality of counts. Hence, is Not Regular.3.Analyze : .
This is simply the language of strings with any number of 's, followed by any number of 's, followed by any number of 's. It corresponds to the regular expression . Hence, is Regular.Therefore, and are regular.Continue learning with Success Tracker
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