GATE | GATE CS 2008 | Question 53

Which of the following are regular sets?

GATECS200854

(A) I and IV only
(B) I and III only
(C) I only
(D) IV only


Answer: (A)

Explanation:  

1.L = {a n b 2m |m, n ≥ 0} is a regular language of the form a ∗ (bb) ∗ .



2. L = {a n b m |n = 2m} is not a regular language. This is a similar language as of {a n b n } which is known to be not a regular language.

3. L = {a n b m |n notEqualTo m} is not regular because there is no way to for finite automaton to remember n, number of as.

4. L = {xcy|x, y ∈ {a, b} ∗ } is a regular language which is concatenation of {x|x ∈ a, b ∗ } on itself with a alphabet c in between. Note: Regular languages are closed under concatenation.

Hence, correct answer would be (A) I and IV only.

 

This solution is contributed by vineet purswani.

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