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GATE | GATE CS 2008 | Question 53

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Which of the following are regular sets?

(A)

{anb2m|n≥0, m≥0}

(B)

{anbm | n = 2m}

(C)

 {anbm n≠m}

(D)

 {xcy | x,y ∈ {a,b}*}



Answer: (A) (D)

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  I and IV only.  


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Last Updated : 28 Jun, 2021
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