Which of the following languages is regular?
(A)
{wwR|w ∈ {0,1}+}
(B)
{wwRx|x,w∈{0,1}+}
(C)
{wxwR|x,w∈{0,1}+}
(D)
{xwwR|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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