GATE | GATE-CS-2007 | Question 31

Which of the following languages is regular? 

(A)

{ww^R|w ∈ {0,1}⁺} 

(B)

{ww^Rx|x,w∈{0,1}⁺}

(C)

{wxw^R|x,w∈{0,1}⁺}

(D)

{xww^R|x,w∈{0,1}⁺}

Answer: (C)

Explanation:

(C) Strings which are the part of this language are either 0w0 or 1w1 where w is any string in {0, 1}* . Thus, language given in option (C) is regular. 

All other languages accept strings which have a palindrome as their substring. 
(A) Strings intersect with 0*110* . 
(B) Strings intersect with 0*110*1 . 
(D) Strings intersect with 10*110* . 
According to pumping lemma, languages given option (A), (B) and (D) are irregular. 

Thus, option (C) is the answer. 

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