GATE | GATE-CS-2009 | Question 11

S -> aSa|bSb|a|b; The language generated by the above grammar over the alphabet {a,b} is the set of
(A) All palindromes
(B) All odd length palindromes.
(C) Strings that begin and end with the same symbol
(D) All even length palindromes


Answer: (B)

Explanation: The possible palindrome generated by above grammar can be of odd length only as there is no rule for S -> \epsilon

For example generated palindromes are aba, aaa, bab, ababa, aaaaa, ..

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